Quantifying the Stimuli of Photorheological Fluids
by
MASSACHUSETS INSMt1TE,
OF TECHNOLOGY
Sarah Woodring Bates
MAY 0 5 2010
B.S., Cornell University (2007)
Submitted to the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degree of
LIBRARIE
Master of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 2010
©Massachusetts Institute of Technology 2010. All rights reserved.
Departm~t of Mechanical Engineering
January 18, 2010
Certified by............................
Anette (Peko) Hosoi
Associate Professor
/7
Certified by..........................
Gareth H. McKiniey'
Professor
A ccepted by .. . . . . . . . . . . . . . . . . r .. . . . . . . . .
David E. Hardt
Chairman, Department Committee on Graduate Theses
ARCHIVES
Quantifying the Stimuli of Photorheological Fluids
by
Sarah Woodring Bates
Submitted to the Department of Mechanical Engineering
on January 18, 2010, in partial fulfillment of the
requirements for the degree of
Master of Science in Mechanical Engineering
Abstract
We develop a model to predict the dynamics of photorheological fluids and, more generally,
photoresponsive fluids for monochromatic and polychromatic light sources. Derived from
first principles, the model relates the irradiance of light source to the evolution of the concentration of a photoactive species within a sample. We show that the limiting time scale
of the dynamics is the rate of photon delivery from the light source. Therefore, we recommend reporting the spectral irradiance of the light source and molar absorptivity, volume,
area of the sample exposed to the beam, and concentration of the photoactive species as a
standard minimum set of variables. Using the nondimensionalized time suggested by the
model, we compare reaction rates of vastly different materials irradiated by very different
light sources.
We validate our model using both published data from literature and our own rheological
experiments. These datasets are shown to collapse onto characteristic curves when properly
scaled. We extend the model to fluids with multiple photoactive components, so that we
may study fluids that have a reversible transition between states accessible by changing the
relative spectral irradiance during operation. We show that considering a light source as
polychromatic is critical to determining the photostationary mole fraction as well as scaling
results between different light sources.
We then use these metrics to determine whether photorheological fluids are appropriate
for application onboard a small autonomous robot. We determine that the two candidate
photoresponsive fluids, a micellar fluid and a nanoparticle-based fluid, are not appropriate
for use in combination with commercial UV LEDs if the speed of transition is a constraint.
However, we suggest features of a fluid ideal for this application and illustrate how techniques such as decreasing film thickness are effective in accelerating the reaction only for
fluids with high initial absorbances. Finally, we suggest how the model aids research into
microstructural dynamics of complex fluids.
Thesis Supervisor: Anette (Peko) Hosoi
Title: Associate Professor
Thesis Supervisor: Gareth H. McKinley
Title: Professor
4
Acknowledgments
I am so grateful to all those, near and far, who helped me complete this thesis. My
advisors have been generous with their time and comments.
Professor McKinley,
thank you for improving my research while also deepening my ability to do research.
Professor Hosoi, thank you for teaching me how to ask succinct research questions
and showing me how to fit them within big pictures.
I also appreciate the technical assistance I received from Dr. Kooi at the ISN with
determining the spectral power of my sources, and Dr. Vella and Dr. Mace from the
Whitesides Group concerning my chemical synthesis quest.
To Team Peko and the NNF, thanks for pointing me in the right direction when
I was looking for whatever I couldn't find. Thanks Tony for the many conversations
about my favorite equation. I'm so glad that I got to have hot chocolate with Sungyon
and do laps around various parts of MIT with Dawn. Randy, Vivek, and Philipp were
great tour guides throughout my introduction to rheology. Many thanks to Matt,
who found no less than three errant semicolons. I'd also like to acknowledge how
much fun it is working with all of the members of the Squishbot team, both at MIT
and at Boston Dynamics. Thank you Jeff, Ahmed, and Maria for making Tuesday
Teleconferences fun. Also, I am grateful that Nadia is still sharing a desk with me
despite the incident with the frogs.
It is with much love that I acknowledge my family. Mom and Dad, thank you for
the phone calls, the emails, the visits. Mom, thank you for reminding me that we are
very brave, and Dad, for telling me that not all things can be integrated. Abby, you
are my sister whom I love and I will always be proud of you.
I also acknowledge the generous support of the Warren M. Rohsenow Fellowship
and the DARPA DSO Chemical Robots program.
AMDG
6
Contents
1
21
Introduction
1.1
1.2
...
Complex Fluids .. .. .. .. ....
...
....
...
...
...
21
1.1.1
Non-Newtonian Fluids .. .. .. ...
...
....
...
.....
22
1.1.2
Active Fluids. .. .. .. ....
...
....
...
.....
22
1.1.3
Photorheological Fluids. .. .. .. .. ...
....
...
.....
25
...
26
...
26
...
1.2.1
SQUISHBot: a Soft Robot .. .. .. .. ...
....
1.2.2
Application Opportunities for Responsive Fluids. .. .. .. ...
1.2.3
Requirements and Relevant Characterization of Fluids
.. .. ...
...
....
1.3
Photorheological Fluids .. .. .. .. ...
1.4
Problem Statement .. .. .. .. ....
1.5
Thesis Outline. .. .. .. .. ....
...
...
...
...
....
....
...
Robotic Application.
...
...
....
....
...
...
...
...
....
...
.
. .
3
.27
...
28
.....
28
...
28
31
2 Photon to Isomerization
....
...
...
....
2.1
Nature of Light. .. .. .. ...
2.2
Interaction of Light with a Molecule. .. .. .. .. ...
2.3
Absorption .. .. .. .. ...
2.3.1
27
...
...
....
Result of Absorption. .. .. ......
...
...
....
...
....
.. .. ...
...
.....
32
.....
33
....
.....
35
36
39
Light as a Massless Reagent
3.1
Energy vs. Intensity: A Chemist's Perspective. .. .. .. ...
3.2
Reaction Rates. .. .. .. ....
3.3
Current Descriptions of Light Source .. .. .. ...
...
...
....
...
....
.....
....
...
40
....
40
....
41
3.4
Quantifying Absorbable Energy Leads to Better Communication
3.4.1
4
5
6
Total Effective Dosage Model .. .. .. ....
...
...
. .
...
44
Quantifying Photon Delivery in a Photochemical Reaction
4.1
Monochromatic Source. .. .. .. ....
4.2
Polychromatic Light. .. .. ...
4.3
Time Dependence of Terms.
...
...
....
.. .. ...
.43
47
...
....
...
....
47
...
....
...
....
50
....
..
51
....
52
....
53
....
...
...
4.3.1
Limiting Case: Time Independence .. .. .. ...
4.3.2
Limiting Case: Time Dependence. .. .. .. ....
....
...
Kinetics and Large Changes with Time
55
5.1
Development of Kinetics within a Theoretical Framework .. .. .. ...
56
5. 1.1
Approximations. .. .. .. ...
56
5.1.2
Nondimensionalization of Monochromatic Case .. .. .. .. ...
58
5.1.3
Validation through Analysis of Existing Literature .. .. .. ...
61
...
....
...
5.2
Extending Solutions to Polychromatic Light. .. .. ...
5.3
Reversible Fluids. .. .. ...
...
...
....
...
...
.....
...
...
.....
....
65
..
69
5.3.1
Monochromatic Case. .. .. .. ....
....
70
5.3.2
Polychromatic Light Affects Photostationary State .. .. ....
73
...
...
....
Selection of Fluids
75
6.1
Robotic Needs .. .. .. .. ...
....
...
....
...
...
.....
75
6.2
Materials .. .. ...
....
...
....
...
...
.....
76
...
...
Photoresponsive Micellar Fluid. .. .. ...
6.2.2
Photoresponsive Nanoparticle Based System. .. .. .. .....
6.2.3
Photoresponsive Hydrogel.
.. .. ...
...
....
...
....
6.2.1
....
...
....
7 Experiments and Polychromatic Behavior
7.1
7.2
Optical Hardware. .. .. .. ...
....
...
7.1.1
Experimental Setup .. .. .. .. ...
7.1.2
Characterization .. .. .. ....
Rheological Testing .. .. .. .. ....
...
78
79
83
...
....
...
76
....
...
....
....
...
...
...
...
....
.....
...
...
...
.....
83
83
88
91
7.3
7.2.1
Rheometer... .. .. .. .. .. .. .. ..
92
7.2.2
Small-Amplitude Oscillatory Shear Flow
92
7.2.3
Procedure... .. .. .. .. .. .. ....
94
Results........ .. .. .. .. .. .. .. .. .. .
7.3.1
7.4
7.5
Analysis.... .. .. .. .. .. .. .. ..
Limitations and Extensions... .. .. .. ....
94
96
106
7.4.1
Dose Experiments.. .. .. .. .. .. ..
106
7.4.2
Temperature Sweep versus Irradiation.
108
Summary.... .. .. .. .. .. .. .. .. ....
112
115
8 Robot Application
8.1
Feasibility of Current Photoresponsive Fluids for Autonomous Robots
115
8.2
Designing Future Photoresponsive Fluids for Fast Switching Times.
118
8.3
Summary of Governing Equations and Other Relevant Quantities.
121
8.4
.....
.
.
Conclusion......
.....
.. .. .. .. .. .. .. .. .. .
124
10
List of Figures
1-1
Active fluids span a range of changing material properties over many
orders of magnitude. While photorheological fluids as a class of materials are not usually reversible, the three outlined in dotted green are
reversible. Liquid Crystal (LC) materials are included for comparison.
The references for these materials are included in Table 1.1. .. .. ...
2-1
24
Illustration of classical and quantum views of the interaction of light
with atoms and molecules. A photon's oscillating electric field interacts
with the electrons in a molecule. The electron cloud oscillates between
asymmetric shapes and, on average, looks like a promoted orbital. Here
a He atom's Is orbital is excited into the 2p orbital. The analogous
molecular a orbital being promoted to either a ar* or 7r orbital is also
shown .. .. .. .. .. ...
2-2
....
...
....
...
...
...
.....
34
A representation of the absorption and emission spectrum of Mercury.
The resonance condition implies that the absorption spectrum is the
.....
photonegative of the emission spectrum [41]. .. .. .. .. ...
2-3
35
The absorption spectrum of the trans- and cis- isomers of Azobenzene. Note that the trans- isomer is more absorptive in the 300-350
nm region, where as the cis-azobenzene is more absorptive in the other
wavelengths [53] ..
.. .. .. ...
....
...
...
....
...
...
36
2-4
Five typical molecules or mechanisms, spiropyrans [48], [6], diarylethenes
[29], photoisomerization [57] [30], photocatalysts [52] [23], and photoinitiators [12], are highlighted in this figure. Photomechanisms are
diverse leading to a broad list of potential practical applications.
3-1
.
.
.
38
Time scales associated with photoreactions span many orders of magnitude. Note that the experimental task of delivering enough photons
for a given reaction is often the limiting bottleneck.
adapted from [55]. .. .. .. ...
3-2
....
...
This figure is
....
...
...
...
42
The study of light is at the heart of many disciplines including radiometry, astronomy, and spectrometry. This chart summarizes the
definitions used in this document. .. .. ...
4-1
...
....
...
....
46
Regimes of application of the reciprocity law, with the number of converted molecules due to absorption on the y-axis and the number of
photons delivered on the x-axis. Reciprocity failure is expected when
....
there is either a small or large photon flux .. .. .. .. .. ....
5-1
54
The evolution of S with t upon monochromatic irradiance depends on
initial concentration So- For small t, S is decreasing linearly with t,
and for large tit decreases exponentially.
5-2
.. .. ...
...
...
...
60
Evolution of Z with t upon monochromatic irradiance describes behavior of modeled photorheological fluids. The family of curves of S
vs t seen in Fig. 5-1 collapse onto a single exponential curve .. .. ....
5-3
61
The metric is applied to the dataset [62] with a slight modification in
the intensity (Io =I)
This is equivalent to 4I)A=313,n
± as the
10
10
quantum efficiency also linearly scales the intensity. The black line is
the theoretical prediction The inset shows the Z vs t using the original
parameters. See Table 5.1. .. .. ...
...
....
...
....
....
62
5-4
Theory over predicts the final photostationary mole fraction as it neglects absorption of Cis-Isomer and requisite Cis-trans isomerization.
Points indicate experimental data [62]; lines are theoretical predictions.
5-5
65
Comparison of experimental data [62] with two theoretical formulations. a) The monochromatic solution is simply scaled to 80% of original value. b) The initial concentration is modified to reflect the pop...
ulation which will not be converted. .. .. .. .. ...
5-6
66
...
The reversible fluid monochromatic formulation is applied. Note that
the I0
6-1
...
=
1/201,, and
Eb
is
103. M01 CM.....................72
A) The absorbance of 1mM of OMCA measured with a Varian Gary 50
spectrophotometer (thickness approximated as 1 mm) B) The viscosity
change seen after irradiation is hypothesized as being due to a change
from long to short worm-like micelles. These figures are reproduced
from [30] ..
6-2
...
.. .. .. ....
...
....
...
...
....
77
....
a) The absorbance of 13mM PAG, 5% Laponite, 6% PF127 measured
with a Varian Cary 6000i spectrophotometer (thickness approximated
as 1 cm) b) The appearance of a yield stress is thought to be from the
formation of a "house of cards" network. Panel b is reproduced from
[51] .. .. .. .. ....
6-3
...
...
....
...
...
....
...
78
....
A multicomponent system described in [54] is photoresponsive due to
oa-cyclodextrin and the photoisomerizable azodibenzoic acid competing
to bind with 'sticky' C12 sidechains on a poly-acrylic acid backbone
6-4
a) UV-vis absorption spectra of 2.5 x 10'
.
80
M ADA collected by a
Shimadzu UV-2500PC spectrophotometer using a 1 cm path length
quartz cuvette. b) A ternary mixture of 5.0 g/L modified hydrogel,
10.0 g/L ca-cyclodextrin, and 1.0 g/L azodibenzoic acid experiencing
repetitive irradiations with UV (closed) and visible light (open) Both
panels are reproduced from [54] .. .. .. ...
....
...
...
...
81
7-1
a) The EXFO S2000 lamp features a closed loop feedback system. A
calibrated intensity sensor monitors the total intensity exiting the lamp
while an iris opens and closes to produce the desired intensity. Panel
adapted from [32].
b) We demonstrate that the irradiance is linear
with the percent of the iris that is open, particularly at smaller desired
irradiances ..
7-2
.. .. .. ...
....
...
...
....
...
...
...
85
Comparison of spectral irradiance between two different total irradiance settings of the S2000 using the Ocean Optics USB2000 Fiber
Optic Spectrometer. Note that the spectrum does not shift between
the two tests despite the difference in total irradiance. .. .. .. .. ...
7-3
86
Uncollimated light sources exhibit variation in relative irradiance both
across the cross-section of the beam (a) and along the path length (b).
a) Illustrates the variation across the cross-section of a beam from a
5 mm diameter waveguide.
b) Illustrates the variation in the peak
irradiance from three waveguides with path lengths greater than 2 cm.
Figures recreated from data supplied by the S2000 manufacturer [33]
7-4
87
The beam from the lamp travels from the waveguide through open air
to the ARES rheometer UV curing fixture where it is redirected by a
mirror through a quartz plate and to the sample. We use two radiometers to measure the irradiance: one that measures the irradiance at the
waveguide endface and one that measures the irradiance of the beam
at the cure site. .. .. .. .. ...
7-5
....
...
...
....
...
....
88
The radiometers systematically report different irradiances measured
at the end of the waveguide. The ratio of the two radiometer measurements is constant over the operating range of the lamp ..
.. .. ....
90
7-6
a) The steady shear viscosity as a function of shear rate before the
sample (50 mM OMCA and 83mM CTAB) is irradiated, fitted with
the Carreau Yasuada model: qo =8Pa.s, A =0.46s, a
=
2.79, ni
-
0.042. b) The dynamic moduli as a function of angular frequency of
the unirradiated sample is fitted with the generalized Maxwell model:
A - 0.41s, g,
7-7
=
19.2 Pa ..
.. .. ...
....
...
...
95
.....
...
a) Time evolution of the steady shear viscosity at different strain rates
for the 50mM OMCA ± 83 mM CTAB solution during irradiation. b)
Repetition of the steady shear test on this sample illustrates the reproducibility of data collected during irradiation. The time constants,
have a mean (B) of .0329 s-' with a standard deviation of 6.8 x 10-3S-1
and the coefficients have a mean (A) of 6.83 Pa.S with a standard deviation of 5.63 x 10-1 PaS ..
7-8
.. .. .. ....
...
...
....
97
....
The moduli change over time as a 50 mM OMCA ± 83 mM CTAB
sample is irradiated. Here, each experiment corresponds to a different
beam irradiance (measured at the cure site). Lower irradiances lead to
longer times required to reach a desired modulus value, while higher
irradiances require less time. .. .. ...
7-9
...
...
....
...
98
....
The shear viscosity as a function of strain rate for different weighted
amounts of OMCA with 60 mM CTAB, re-plotted from Ketner et al
[30]. The fit is to a simplified Carreau Yasuda model with the empirical
constants listed in Table 7.3. .. .. .. ....
...
...
....
99
....
7-10 Exposure of 50 mM OMCA + 60 mM CTAB sample by an uncharacterized UV lamp for set periods of time. A Maxwell model is fit to
101
..
each curve with parameters listed in Table 7.4 .. .. .. .. .. ...
7-11 Data describing the relationship between weighted amounts of transOMCA + 60 mM CTAB concentration and zero shear viscosity reported in Ketner et al [30]. Using an exponential fit, we approximate a
relationship between the concentration of the OMCA and the viscosity
to be used in our comparisons between experiment and theory.
.
.
.
103
7-12 Estimation of final concentration of OMCA from the rheological data
taken and relationship derived from Fig. 7-11. This is then compared
to our model's prediction of the concentration given the experimental
conditions ..
.. .. ...
...
....
...
...
....
...
...
..
104
7-13 Comparison of complex viscosity, 77*, experimental data with theoretical prediction. The concentration and complex viscosity axis have been
scaled to reflect the empirical relationship between concentration and
n*.........
.. .. .. .. .. .. .. .. .. ....
...
105
......
7-14 The evolution of moduli during irradiation with time axis scaled to t'.
In contrast to Fig. 7-8, the data has collapsed onto characteristic curves. 107
7-15 After doses of irradiation, the sample recovers. Open triangles indicate that the measurements were taken despite being below the stated
torque resolution of the ARES rheometer. The initial evolution of the
viscosity is compared with the theoretical prediction of the concentration. 109
7-16 The moduli are examined after doses of irradiation are delivered. After
the irradiation is stopped, the sample partially recovers. .. .. .. ..
110
7-17 The measurement of complex viscosity from the dose experiments is
compared to the theoretical prediction of concentration through the
process described in section 7.3.1 .. .. .. .. ...
...
...
111
......
7-18 Comparison of dynamic moduli of a 50 OMCA -+ 83 CTAB sample
undergoing a temperature ramp without irradiation (bottom axis) and
under irradiation causing the concentration at constant temperature of
trans-OMCA to decrease (top axis). The scaling of the two axis is 1.23
mM per 'C. During the 100 second interval of irradiation the absorbed
energy was calculated to be approximately 1 J.. .. .. .. .. ...
8-1
..
113
Spectral power of a UV-LED (FOX) measured by the Ocean Optics
USB2000 Fiber Optic Spectrometer.. .. .. .. .. ...
...
......
116
8-2
The evolution of the material composition during irradiation from an
LED for two candidate fluids with a photoactive species concentration
of 50 mM OMCA and 13 mM PAG respectively. Note that both fluids
require hours of irradiation to convert half of the photoactive species.
117
18
List of Tables
...
...
...
....
...
23
....
30
1.1
References for Figure 1-1. .. .. .. ...
1.2
Frequently used variables. .. .. .. .. ...
3.1
Descriptions of optical setups are not standardized and vary between
....
...
....
authors. This table presents five typical optical setup descriptions from
literature, [171, [30], [46], [54], [61], and one industry data sheet, [1].
43
5.1
Experimental parameters from Zimmerman et al. [62]. .. .. .. ....
63
5.2
Dimensionless groups and solutions for irreversible fluids irradiated
with a monochromatic source (1), a polychromatic source for a fluid in
the large absorbance regime (2 a) and in the small absorbance regime
(2 b). .. .. .. ...
5.3
...
....
...
...
68
.....
...
...
...
....
73
...
...
....
...
...
.....
....
78
Comparison of specifications of the Accu-Cal 50 radiometer and the
R2000 Radiometer .. .. .. ...
7.2
...
Composition of four batches of OMCA±CTAB solutions prepared for
experiments .. .. .. .. .. ...
7.1
...
Comparison of experimentally observed [62], and predicted cis-isomer
photostationary states. .. .. .. ....
6.1
....
....
...
...
....
...
89
...
Relevant time constants, t' and t, reported as experimental description
91
given S2000 polychromatic source and candidate fluids .. .. .. ....
7.3
Fitting parameters for simplified Carreau Yasuda model of data shown
in Fig. 7-9 of weighted amounts of OMCA and 60 mM CTAB
. .
.
.100
7.4
7-10
Fitting parameters for Maxwell model for data shown in Fig.
and the resulting zero shear viscosity. The sample is initially 50 mM
OMCA + 60 mM CTAB and then undergoes irradiation for the time
specified. .. .. .. .. .. ....
8.1
...
...
....
...
.....
....
100
Relevant time constants, t' and t, of 8pL of micellar fluid irradiated
with LED compared to 160 ,atL of nanoparticle fluid irradiated with
S2000. .. .. .. .. ...
....
...
...
....
...
....
.....
115
8.2
Parameters which tune how quickly the sample reaches 95% conversion 120
8.3
The energy absorbed and the number of molecules converted during
an exposure period. .. .. .. ....
8.4
...
...
....
...
Summary of governing equations for irreversible and reversible fluids
for monochromatic and polychromatic sources (4)=1). .. .. ...
8.5
122
..
Summary of solutions and dimensionless numbers for illumination of
irreversible fluids ()I1) . .. .. ...
8.6
122
......
...
....
...
...
123
.....
Summary of approximate solutions and dimensionless numbers in the
limit of small absorbances for illumination of reversible fluids (4)I1)
.
123
Chapter 1
Introducion
Photorheological fluids, or fluids that change their flow properties in response to light,
are interesting not only academically but also for their potential applications. With
the increasing availability of light emitting diodes (LED) at new and smaller wavelengths, photoresponsive materials may make their way into a broad range of devices.
This will only happen if researchers, designers, and manufacturers can systematically
quantify the energy consumption and transition time of these materials in a variety
of environments. In this thesis, we will propose a model describing the time evolution
of the response of the material to light. We will see that this is an important step in
determining the feasibility of a particular fluid for a specific application.
1.1
Complex Fluids
A fluid is defined as a material in which an applied stress gives rise to a constant strain
rate as opposed to a solid where the same stress would lead to a constant strain. A
familiar example of this definition is a Newtonian fluid:
0-
(1.1)
1.1.1
Non-Newtonian Fluids
Many fluids can be described with the simple linear relation in 1.1. However, many
fluid-like materials do not show this behavior and are therefore termed 'Non- Newtonian'.
Non-Newtonian fluids often have a viscosity that depends on the applied stress or
strain rate, yield stress fluids are an example of the former and shear thinning and
shear thickening fluids of the latter. Yield stress fluids, like toothpaste and shaving cream, behave like solids when stressed below a certain stress, called the yield
stress. Shear thinning fluids have a lower viscosity the higher the strain rate applied
and vice versa for shear thickening fluids. Non-Newtonian fluids can also fall on the
visco-elastic spectrum with some part of their stress response being related to the
strain applied rather than the strain rate. Other complex fluids include thixotropic
fluids whose microstructure changes over time, leading to a history dependent viscosity. These fluids offer a glimpse into the rich behavior of fluids beyond the simple
behavior of the Newtonian fluid.
1.1.2
Active Fluids
In all of the examples above, the rheological properties of the fluid are fixed to the
relevant dynamic conditions. We define active fluids as those fluids whose rheological properties are dependent on some external applied field. With these fluids, the
experimentalist has more control over the response of the fluid even if the dynamic
conditions like strain rate or applied stress are fixed. In this way, the fluid becomes
a more 'engineerable' material for a given application.
These active fluids have found their way into many viable commercial products,
such as hot glue guns. Car suspensions and clutches also take advantage of magnetorheological (MR) fluids and electroheological (ER) fluids. Application of a magnetic
field or an electric field respectively causes the small particles suspended in these fluids to align and give structure to the fluid
([431,
[45]). At high applied field strengths,
both ER fluids and MR fluids behave more like solids below a yield stress. Thermorheological fluids, such as solder and hot glue, have a low melting temperature. When
heated, the internal temperature is raised and the viscosity of the fluid changes drastically. Another class of active fluid, photorheological (PR) fluids undergo a chemical
reaction, upon the application of a particular spectrum of light, which changes the
fluid on a molecular level leading to new rheological properties.
While these fluids all possess the same desirable nature, in situ tunable rheological
properties, they are so different phenomenologically that they are difficult to compare
for design purposes. Not only are the resulting rheological properties hard to compare
(such as a change in yield stress versus a change in viscosity), but the required stimuli
themselves are in distinct physical domains. If we consider designing a mechanism or
sensor using an active fluid, then it may be that we wish to find a fluid that maximizes
the difference between the two rheological states. Fig. 1-1 illustrates the magnitude
of property changes for a variety of active materials.
Table 1.1: References for Figure 1-1
#
1
2
3)4 8-10,16
5
6
7
11
12
13
14
15
17
18
19
20
21
22
23
24,25
26,29
27,28
Reference
Tomatsu et al. [541
Botella et al. [5]
Ewoldt [44]
Haines et al. [24]
Wen et al. [60]
Alvarez-Lorenzo et al. [
MRF-140CG [14]
MRF-122EG [13]
Schmidt et al. [49]
Matsumoto et al. [37]
Steeman et al. [50]
Khan et al. [31]
Deshmukh et al. [17]
Ketner et al. [30]
Sakai et al. [46]
Dasgupta et al.[15]
Espin et al. [20]
Naciri et al. [39]
Verney et al. [56]
Cook et al. [12]
Jadzyn et al. [26]
I
I
I
-I.--
-
I
I
>
0
I
*
I
I I
I
I
I
I
I I
Ys: Yield Stress
11: Viscosity
G': Storage Modulus
G": Loss Modulus
G.*: Complex Modulus
E: Youn g's Modulus
Ea: Apparent Modulus
I0-
aPR
I-
EER
*MR
*LC
2
4
6
II
C
r-CU
Eli
8 10 12 14 16 18 20 22 24 I,26 28
Figure 1-1: Active fluids span a range of changing material properties over many
orders of magnitude. While photorheological fluids as a class of materials are not
usually reversible, the three outlined in dotted green are reversible. Liquid Crystal
(LC) materials are included for comparison. The references for these materials are
included in Table 1.1.
There are many other relevant design considerations that are not captured by this
figure. For instance, some materials go from a property possessing a smaller value
to possessing a larger value with an applied field. Others show the reverse behavior.
We consider the former a 'positive gain' material and the latter a 'negative gain'
material. Choosing one or the other is an important application dependent decision.
For instance, for a glue whose purpose it is to hold an object in place, we would
want its resting state (zero field) to have a high yield stress. Only when we wish to
move the object, do we want to apply a field and lower the yield stress. Therefore
a negative gain material is most appropriate, so that we do not spend energy on
maintaining the base state. This definition also assumes that we must continually
apply energy to achieve one of the two rheological states. While this is true for the
simplest mechanisms with TR, ER, or MR fluids (though permanent magnets [22],
and capacitive circuits expand the stimuli possibilities), it is often not true for PR
fluid.
1.1.3
Photorheological Fluids
Photorheological fluids change on a chemical level in response to light stimuli. The
majority of PR fluids then stay in this new state for a long period of time until they
relax to their more energetically favorable states (if at all). In this way, they act
more like a switch than the other materials. If the application constrains the energy
available, then this switching ability may be desirable. This is only desirable if the
energy input required to switch is less than the energy required for a comparable
material during the application lifetime. Upon first evaluation, PR fluids seem to
require large amounts of power over large time scales to switch. However, as will be
detailed in this thesis, the limited information that is presented in literature (often the
wattage of a laboratory lamp) is not detailed enough to do an energy calculation that
reflects realistic energy consumption. Determining what is a complete description of
the light source will become a focus of this thesis.
1.2
Robotic Application
As we have mentioned, the evaluation of these fluids can be strongly applicationdependent. Our application is in the field of robotics. Fluids are not often featured
in mechanisms beyond fueling, cleaning or lubricating roles with the exception of
hydraulic and underwater robots.
As an active component, they find themselves
under the same expectations as other components such as being t ask- appropriate,
energy-efficient, lightweight, and robust. In the developing field of "Soft Robotics,"
where robots morph and deform, we imagine less traditional materials like foams
and composites will be valued for their low moduli. If fluids could be manipulated
successfully they also would lend themselves well to a robot which needed to be able
to slither through tight spaces. Active fluids could play an important role in this class
of robots.
1.2.1
SQUISHBot: a Soft Robot
Our team has been developing a robot, SQUISHBot, in response to the Defense Advanced Research Projects Agency (DARPA) ChemBot call for proposals [42]. Ideally,
the ChemBot, approximately the size (but not necessarily the form-factor) of a regulation softball should demonstrate the ability to:
* travel a distance of 5 meters at a speed of 0.25 meters/minute;
* achieve a 10-fold reduction in its largest dimension; and
9 traverse through a 1 cm opening of arbitrary geometry and reconstitute its
original size and shape, in 15 seconds.
Obviously these requirements necessitate the development of a novel soft robot.
SQUISHBot is in part a next generation version of the Robosnail, first developed
by Brian Chan [7]. This robot mimics the adhesive locomotion style of a snail with
rigid sliders and a specially engineered yield stress fluid or slime [21].
Our team
plans to incorporate the unique locomotion style of the Robosnail with tunable stiff-
ness composites to achieve deformability. Both this locomotion style and composite
approach provide opportunities to incorporate active fluids.
1.2.2
Application Opportunities for Responsive Fluids
The slime played a central role in past instantiations of the Robosnail [8]. A large
yield stress, while ideal for locomoting heavy robots up walls, would require a large
pumping force and a large pump. In the past, the Robosnail did not have the need to
be autonomous and so the slime was painted onto the surface by hand before placing
the Robosnail on top of it. As the Chemflot must be autonomous, the slime has a
new requirement of being pumpable. Unfortunately, the very property that would be
optimal for locomotion is decidedly sub optimal for pumping. An active fluid with a
switchable yield stress would be ideal as the fluid could be pumped when the slime
has a low yield stress and used as an adhesive when the yield stress is large.
In tunable stiffness beams, the fluid plays a more structural role than in the active
slime. SQUISHBot employs passively compliant of foams in combination with a single
actuator, a spooler motor [10]. The foam contains an active fluid such as wax which
either melts and leads to a compliant structure, or which hardens and maintains its
shape upon loading [9].
1.2.3
Requirements and Relevant Characterization of Fluids
Both of these applications would benefit from a fluid with a large difference between
rheological states. It would also be desirable for the fluids to move reversibly between
states, although the slime application allows for a disposable fluid as a lesser substitute. Of most relevance are the constraints placed on the energy consumed by, and
the cycle time of, these fluids. The velocity of the robot may well be limited by the
timescale of these fluids moving between states. If the cycle time of the fluid is longer
than a couple of minutes, the use of that fluid quickly becomes impractical. Related
to this, the energy required to stimulate these active fluids must be small enough to
allow for continued operation of the robot for the length of its required run. SQUISH-
Bot is a small battery powered robot. Therefore quantifying the energy requirements
of these fluids is a primary task when determining the feasibility of using a specific
fluid onboard a robot.
1.3
Photorheological Fluids
Photorheological fluids are used in a narrower set of applications than the other classes
of active fluids such as UV curable glues. Despite this, they have definite advantages.
While ER and MR fluids must often be sandwiched between two plates, PR fluids can
be switched by a light source at a single location, possibly even physically removed
from the fluid. PR and TR fluids are also generally isotropic. Due to the chemical
nature of their property change, they can have the largest property changes that
remain after the stimuli is removed as seen in Fig. 1-1. Long switching times and
large energy demands may be prohibitive drawbacks. These disadvantages remain
largely uncharacterized.
1.4
Problem Statement
In this thesis we will seek to quantify the time and energy required for a photoresponsive fluid to switch between two states. We will then apply this characterization to
determine whether a few selected fluids are appropriate for robotic application given
available light sources.
1.5
Thesis Outline
In chapter two, we will look at how molecules interact and absorb light. In chapter
three, we will look at how quantifying the number of photons can be used as a metric
to characterize energy consumption, light sources, reaction rates, and design efficiencies. In chapter four, we develop a framework for relating the number of photons to
these quantities through fundamental relationships and experimentally measurable
quantities. In chapter five, we expand this model to analyze kinetics for situations
involving monochromatic or polychromatic sources in conjunction with reversible or
irreversible fluids. We also compare the models to data published in literature. In
chapter six, we select three candidate materials for robotic application.
In chap-
ter seven, we describe a set of rheological experiments performed while irradiating
the material with a polychromatic light source and discuss the results. In chapter
eight, we conclude with a brief discussion about the feasibility of using these fluids in
conjunction with commercially available UV LEDs onboard an autonomous robot.
Variable
Table 1.2: Frequently used variables
Value or Units
Definition
3.00 x 108 m
S
speed of light in a vacuum
h
J S
Planck's constant
6.26 x
1
Na
Avagadro's Number
6.022 x 1023 M01
m
A
wavelength of light
wn
radiant
intensity prior to sample
I, Ii, I(A)
sr nm
w
transmitted radiant intensity after sample
sr nm
Iit
w
incident radiant intensity of monochromatic light A
sr
w
transmitted radiant intensity of monochromatic light A
sr
w
absorbed radiant intensity of monochromatic light A
IaA
sr
w
spectral irradiance over an area prior to sample
Ir, Iri, Ir (A)
m2 nm
w
incident irradiance of monochromatic light A
Ira\
number of photons
Nphotons
[]
NaA
number of photons of wavelengthA absorbed
[]
Nm,\
number of molecules absorbing photons of wavelengthA
E
energy
J
energy of absorbed photons of wavelength A
EaA
A(A)
absorbance
[]
AA
absorbance given the incident light is wavelength A
[1]
quantum efficiency of material
<b <(A)
[]
quantum efficiency at wavelength A
[L]
molar absorptivity of material X
E, EX, E(A)
moi cm
L
molar absorptivity at wavelength A
mol Cm
Pa s
viscosity
Pa s
zero shear rate viscosity
7o
storage modulus
G1
Pa
loss modulus
Pa
f
m
path length through a sample
G
sr
solid angle of beam
incident area of beam
Areaj, Ai
m2
V
volume of a sample
L
t
time
s
experimental
time
texp
s
duration
T
concentration
of
photoactive component
[S]
concentration of X
[X]
L
mol
initial concentration of X
[Xo]
molar fraction
rad
frequency
of oscillation
S
1
strain rate
S
C
10- 34
Chapter 2
Photon to Isomerization
In this chapter we describe the mechanisms behind photorheological fluids starting
with how they absorb light. Absorption is a key step in stimulating photorheological
fluids, and describing this step will lay the ground work for developing a metric that
is useful for engineers and acceptable to chemists.
There are two different perspectives of importance when evaluating the stimuli of
photorheological fluids. As an end user, the robotocist is interested in power requirements of the stimuli, time scales associated with the transition of states, material
properties, and the lifetime of each state. While maximizing lifetimes and material
advantages is a concern, he is probably interested in minimizing the transition speed
and the power input to the lamp. To do this, the robotocist must match the light
spectrum from a lamp to the spectrum that "activates" the fluid. For all intents and
purposes, however, the robotocist wishes to treat the fluid as a black box.
The chemist however has a perspective informed by scientific inquiry rather than
utility. The chemist seeks a deep understanding of the physics and chemistries of
reaction and has already defined and characterized certain aspects of this process.
However, these definitions can be unwieldy and often far removed from bulk characterizations useful to the engineer.
One of the goals of this thesis is to provide the engineer with the tools required
to design with these sophisticated fluids. The tools however must be consistent with
accepted chemistry paradigms. This criterion has the advantage of providing a frame-
work such that experiments in one field can be used and compared in another field.
Even though our application demands an engineering perspective, it may be easiest
to start "at the beginning" with a chemical picture of the major actors in this reaction.
All photorheological fluids are stimulated by light, so we begin with the nature of light.
2.1
Nature of Light
Modern conceptions of light include both the wave-like nature and particle-like nature
of light. Einstein proposed this picture in support of Planck's suggestion that the
energy of a light wave was quantized [19]. Light can be described as both having
a wavelength (a wave property) and can be related to momentum through Planck's
constant (a fundamental constant related to a particle or quantum phenomena). This
special light particle, or photon, has a quantized energy:
E =
hc
A
(2.1)
where E is the energy of a photon, h is Planck's constant, c is the speed of light,
and A is the wavelength of the photon. Turro et al. [55] describes how the wave
nature and the particle nature relate:
"In this model, light is part of the electromagnetic field that is spread
out and fills the entire universe; the wave can be considered to propagate
through the universe "at the speed of light." When light is absorbed by
a molecule, the "spread out" wave is suddenly "localized" in the small
space occupied by the molecule."
Because we are interested both in emission and absorption, we encounter both natures
in our study. As Turro summarizes, "Thus a photon behaves more like a wave when
it is not strongly interacting with matter and more like a particle when it is strongly
interacting with matter." When describing chemical reactions, this particle view of
light will prove to be useful.
2.2
Interaction of Light with a Molecule
Since we are interested in the response of the fluid to light, a closer look at how light
interacts with a molecule is warranted. To a molecule, the light wave is mostly an
oscillating electromagnetic field that interacts with the electrons of a molecule.
F
=
eE + e (Hv)
(2.2)
C
Here F is the total force exerted on an electron, eE is the electrical force,
e(Hv)
is the
magnetic force, v is the velocity of an electron and c is the speed of light. Because the
maximum speed of an electron is small compared to the speed of light, the magnetic
component of the total force is small compared to the electrical component. The total
field interacts with the molecule's electrons by exchanging energy through resonance.
For this process to happen, three conditions must be met:
1. 6E = hv, the energy required for transition between the ground and promoted
orbital must be equal to the energy of the incoming photon. This is a statement
of energy conservation. It can be restated as Einstein's resonance condition:
during a transition, the electric dipole moment of a cloud will resonate at frequency v =-EhE2 . This must equal the frequency of incoming electromagnetic
radiation for a transition to occur.
2. Momentum must be conserved. There must be an exact match between the
angular momentum gained or lost (captured by the creation or destruction of
a node in the electron cloud, see Fig. 2-1) and the angular momentum of the
photon.
3. The transition dipole moment created by the interaction of the electron with
the electromagnetic field must be finite.
If these conditions are satisfied, the oscillating electrical field will reshape the electron
distribution and cause it to oscillate between asymmetric shapes as the electron cloud
is alternatively attracted and repelled by the wave. The nucleus does not resonate
Clas sical Light Atom Interaction
H
E
H "
Time Averaged (Quantum Orbits) Light Interaction
(bonding)
1s
(anti-bonding)
2p
Atom
Molecule
Figure 2-1: Illustration of classical and quantum views of the interaction of light with
atoms and molecules. A photon's oscillating electric field interacts with the electrons
in a molecule. The electron cloud oscillates between asymmetric shapes and, on
average, looks like a promoted orbital. Here a He atom's Is orbital is excited into
the 2p orbital. The analogous molecular o orbital being promoted to either a o-* or
7r orbital is also shown.
with the same frequency as the electron cloud. The time average of this oscillation
about the nucleus looks like a promoted orbital. Fig 2-1 details this process for a
single He atom and for a simple molecule. For each photon absorbed by a material
only one molecule is activated, a restatement of the resonance condition known as
the Stark-Eistein law. In rare cases two photons can be absorbed to activate one
molecule, however this occurs mostly in highly controlled laboratory settings.
Absorption Spectrun of Hg
Emission Spectrum of Hg
Figure 2-2: A representation of the absorption and emission spectrum of Mercury.
The resonance condition implies that the absorption spectrum is the photonegative
of the emission spectrum [41].
2.3
Absorption
Now that we understand the theoretical picture of light absorption, we discuss how
to quantify this phenomenon in experiments. An experiment measuring the optical
density of a sample is a standard way of measuring the absorbance of the sample. The
intensity of the light falling on a sample and the intensity of the beam transmitted
through the sample are measured. The log of this ratio is termed the optical density.
The higher this number, the larger the amount of incident light absorbed. If we
divide this number by the path length of the light, i.e. the thickness of the sample,
and the molar concentration of absorbing molecules, we find the molar absorptivity.
This is a fundamental molecular property and has units of area per mole (often
reported
L
). These relationships are characterized by the Beer-Lambert law in
the following equation:
E==
1log({
t
l[S]
(2.3)
In Eq. (2.3), [S] is the concentration of the absorbing species, the molar absorptivity
is e (also known as the molar extinction coefficient), the thickness of the sample is 1,
the incident intensity is i and It is the transmitted intensity.
One of the implications of this molecular picture of absorption is that the absorption must be wavelength (or frequency) dependent in order to satisfy the resonance
condition. To communicate which wavelengths the molecule absorbs, we can plot the
molar extinction coefficient (or its log, as the value varies widely) as a function of
wavelength. This type of plot is called an absorption spectrum.
Given the resonance condition's limit on absorbable frequencies we would expect
that the absorbance spectrum would only have a few fairly sharp peaks corresponding
4.5
4.0 *
%F
3.5 -
..
-
o 3.0
*
2.52.0
250
-
-
-
300
350
400
Wavelength (nm)
450
Figure 2-3: The absorption spectrum of the trans- and cis- isomers of Azobenzene.
Note that the trans- isomer is more absorptive in the 300-350 nm region, where as
the cis-azobenzene is more absorptive in the other wavelengths [53].
to the allowed wavelengths. This is the case for atomic spectra as the energy states
are discrete. Fig. 2-2 illustrates the absorption spectrum of Mercury. However, the
molecular absorption spectra have broader absorbance bands because of the many
allowed rotations, vibrations, and collisions that can store energy. An absorption
spectrum of a typical photorwsponsive compound, Azobenzene, is given in Fig. 2-3.
2.3.1
Result of Absorption
The first law of photochemistry, or the Grotthus-Draper law, states that a photon
must be absorbed to cause a photochemical change.
With this extra amount of
energy, a variety of things can happen. The molecule may be more reactive or the
new electron distribution can allow a trans-cis isomerization to occur. This step in
the process can be characterized by a rate constant, describing the primary process or
any secondary processes occurring if present. There are a variety of photomechanisms
each specific to the molecule, and reactants.
Not every absorbed photon leads to a reaction and is subsequently emitted. This
phenomena can be quantified with the quantum efficiency (<D) of the reaction. The
quantum efficiency represents the probability that an absorbed photon of a particular
wavelength effects a change in the molecule.
The following figure illustrates a few molecules and their uses before and after
transition. Spiropyrans(a) are an example of a class of photochemicals called chromophores. These molecules can be found in automatically tinting indoor/outdoor
glasses. This spiropyran can selectively bind Cu2+ or Co2+ when irradiated by visible
or ultra violet light. Diarylethenes (b) can used as electrical switches and photocatalysts (d) can be used to break down volatile organic chemicals, change surface
tensions, and alter a solution's pH. Of particular interest for our application are
molecules that affect mechanical properties such as moduli, creeping behavior, and
bulk deformation. This can be achieved with molecules that cleave crosslinks such
as some photoinitiators (e), and molecules that reassemble into different configurations after having a conformal change in molecular geometry (c) typical with some
photoisomerizations.
The variety of mechanisms provides a challenge for bridging the gap between
engineer and chemist. Each one has a unique characterization, yet the engineer prefers
to compare a bulk property. Individual chemical mechanisms are beyond the scope
of this document and will be omitted in favor of a black box approach. To ensure
validity, we will examine the mechanisms for select candidate fluids explored in a later
section. We will use the fact that these diverse mechanisms all absorb photons to
quantify whether a light source is appropriate for a fluid and to monitor the progress
of a reaction. The fact that we can measure how easily a material absorbs photons
leads to the success of the experimental framework suggested.
a)
gb)
Spiropyrans
c) Trans-Cis Isomerization
Diarylethenes
temw
4~
I
Cu"---------
Co
binding
I
sites
.
----
d) Photocatylsts
-
M
L
Deora
Moduli, Deformation
Conductance
----------
----..
e)
Photoinitiators
Ta4
AM
pH, Surface Tension
Photoplasticity
Figure 2-4: Five typical molecules or mechanisms, spiropyrans [48], [6], diarylethenes
[291, photoisomerization [57] [30], photocatalysts [52] [23], and photoinitiators [121,
are highlighted in this figure. Photomechanisms are diverse leading to a broad list of
potential practical applications.
Chapter 3
Light as a Massless Reagent
Since cataloging all of the molecules and their reactions would be difficult even for an
experienced photochemist, we take a different approach. All photoreactions consume
a "massless reagent" - light. We wish to pick a metric that we can report that would
allow an engineering comparison of the different photomechanisms for design purposes. Each mechanism, however, requires a different wavelength of light. We could
report the most effective wavelength of light, the wavelengths used in experiment, the
emission profile, the quantum efficiency, the absorbance spectrum, or a number of
other quantities which are wavelength dependent. All of these variables characterize
some part of the molecule or reaction, an ideal experiment, or a combination of both.
When comparing stimuli of fairly different natures previously, we discussed active
fluids in terms of an energy metric, specifically the energy consumption of each class
of fluids. We will take the same approach here with the expectation that this will
be easier as energy is directly related to the frequency of light and indirectly to the
intensity of light. There are many energies available as metric candidates. We could
report the energy per photon, the total energy absorbed by the material, the energy
associated with the flux of photons from the beam, or the energy required to power
the lamp. In this chapter, we lay the chemical ground work for the decision to use a
metric related to the total energy absorbed by the material, a quantity that depends
on the matching of the emission spectrum of the light source with the absorbance
spectrum of the material.
3.1
Energy vs. Intensity: A Chemist's Perspective
The energy absorbed by a material as a metric is appealing from both the chemist's
and engineer's perspective. For the engineer, the energy absorbed is closely related
to the energy delivered by an external source. For the chemist, the energy absorbed
can be used to count the number of absorbed photons
EAbsorbed
(3.1)
Aabsorbed
The number of photons (Nphotons) is proportional to the energy absorbed (Eabsorbed)
by the ratio of the wavelength of the photons (A) to Planck's constant h and the
speed of light (c). This ratio is the energy of a single photon.
While a chemist would argue that the most important energy is the energy per
photon, from the argument above, we can see the experimental relevance of the absorbed energy. By focusing on the absorbed energy rather than total energy available,
we avoid the ambiguity associated with the fact that red light may deliver to atoms
which select photons by wavelength less "useful" energy than a less intense blue light
despite being more energetic than blue light.
After the historical misconceptions
about the energy of a beam (intensity) versus the energy in a single photon, descriptions of the energy delivered by a beam have been de-emphasized in literature.
However, a beam delivers a finite number of photons in finite time; a chemically
relevant (and countable number) that impacts rates of reaction.
3.2
Reaction Rates
One mole of a single wavelength of photons is called an 'einstein' and carries varying
amounts of energy. If these photons correspond to a low frequency as in the radio
frequency (RF) range with wavelength 1 meter, the einstein carries 4 picojoules; if
they correspond to a ultraviolet (UV) range wave with a 365 nm wavelength, 32
kilojoules. Experimental equipment can deliver photons at vastly different rates even
for a given wavelength of light. A UV laser that delivers 5 Watts of 365 nm light
would take almost 2 hours to deliver an einstein of photons to the surface of the
sample. UV LEDs, a recent technological advance, have a typical power output of
50pW, requiring over 20 years to deliver the same einstein of photons. Clearly this has
chemical and engineering repercussions. In fact, this delivery mechanism generally
represents the limiting timescale of an experimental setup involving a photoreaction.
The current practice of reporting times of transition between observable states is
misleading if the power and the spectrum of the lamp are not also submitted. This
follows from Stark-Einstein's law requiring one photon for each absorbing molecule.
Therefore we can consider photons to be a limiting reactant. All of the other relevant time scales are significantly smaller than the hours and days represented by
the delivery timescale. Fig 3-1 summarizes the relative event rates. The time scale
governing absorption is less than 10 microseconds. The lifetime of a electronically excited organic molecule is bounded by fluorescence at 10-
9
seconds and 10-
5
seconds
if it is a singlet state (spin forbidden transitions can be up to 10 seconds). Even in
self assembling systems where active molecules must diffuse and assemble, the time
constants related to diffusion (3ms) and assembly (hours) are much less than 20 years.
The rate of reactions reported in literature would be highly dependent on the rate
of photons delivered to the sample and subsequently absorbed. Therefore, there is a
need for useful reporting standards for light sources.
3.3
Current Descriptions of Light Source
Scientists report experimentally accessible descriptions of their light sources. These
descriptions are not standardized and provide scattered information about the light
source. Examples of light source descriptions from literature and industry are provided in Table 3.1. While each paper has its own goal, scientists usually strive to
provide complete descriptions of their apparatus so that future scientists may use
the same data for related but different purposes. These scientists must be guided by
a combination of importance of the description and experimental ease of obtaining
that description, whether measured by cost, time, or specialized instruments required.
I
4
11d9
0e
I
l
10-15
femto
10-9
nano
I
|
I0-3
milli
103
kilo
109
giga
seconds
Log (time scale)
Figure 3-1: Time scales associated with photoreactions span many orders of magnitude. Note that the experimental task of delivering enough photons for a given
reaction is often the limiting bottleneck. This figure is adapted from [55].
Therefore, sympathizing with this tradeoff, we wish to find a description of the light
source that not only satisfies chemist and engineer but can also be attained with
minimal additional effort compared to what is currently reported.
As we have seen from our chemical picture tour, what matters about the lamp is
how many of the most absorbable photons can reach the sample. None of the descriptions in Table 3.1 summarizing published descriptions of optical setups can be used
to recreate this metric. The bulb wattage is irrelevant except as a ballpark measure
of relative intensity between laboratories. Both the lamp element and the wavelength
range hint at the emission spectrum present at the sample, but are usually presented
in a way which obscures the precise relative intensities. The irradiance and duration
of cure tell us how strong and how long the cure was, while the experimental path
length acknowledges an uncollimated light source. Unfortunately, the community has
not captured a relevant metric with any of these descriptions.
Deshmukh et al.
Ketner et al.
Sakal et al.
V/
Tomatsu et al.
Yan et al.
3M LC-1222
adhesive
Vol
Table 3.1: Descriptions of optical setups are not standardized and vary between
authors. This table presents five typical optical setup descriptions from literature,
[17], [30], [46], [54], [61], and one industry data sheet, [1].
3.4
Quantifying Absorbable Energy Leads to Better Communication
Here we present absorbable energy as a standardizing characterization of a photon
source. As mentioned previously we can obtain the number of photons of a given
wavelength present in a beam. This holds for both monochromatic and polychromatic
light sources as we can separate out the energy contributions from each wavelength.
To do this, we must know the spectral composition of the beam. Fortunately, we can
obtain the distribution of wavelengths of a beam with a spectrometer, or from the
manufacturer. If we measure the total power (J/s) of the beam with a radiometer, we
can now determine how many photons within a range of wavelengths are reaching the
sample per second. The irradiance must be measured at the sample for incoherent
sources. Alternatively, the path length can be used to calculate the incident energy on
the sample using energy conservation. The initial intensity 1o measured at some small
distance from the source, lessens so that at some farther distance (r) the intensity has
dropped to I;
-0 =
To
-
(3.2)
T
To duplicate experiments for a given material, all of the variables put forward so far
would have to be replicated. If a lab cannot duplicate both the relative energies and
distribution in wavelength of the source it can use the absorbing materials as reliable
filters to compare results. When filters are used, the transmission can be calculated
by convolving the filter specs with the measured emission spectrum. As we have seen,
materials accept only very specific photons based on their absorbance spectrum. We
can apply this absorbing material to our emission spectrum in the same fashion as
with filters and calculate the delivered absorbable energy. This is now a single number
that any scientist with the absorbance spectrum of the material can use to calculate
the number of photons actually delivered.
Any previously reported rates can be
scaled with the size of the lamp and a radiometer easily recalibrates the metric during
experimental testing. We can even compare these rates to other experiments with
different photochemicals involved as desired by an engineer or designer. Engineers can
then quantify the design tradeoffs associated with using different lamps with respect to
rates of reaction, energy consumption, and source suitability for a particular material.
To summarize, where before it was a challenge to make meaningful comparisons
outside of a single paper, we can now potentially compare rates of response and
material behavior between experimental setups, cure conditions involving high and
low power lamps, and even between different materials if we quantify the absorbed
energy during our experiments.
3.4.1
Total Effective Dosage Model
The total absorbable dosage metric as a reporting metric for scaling light sources has
been suggested in the literature [35]. In this and other studies, Martin uses this "total
effective dosage model" to look at polymer degradation from the sun [34). By using
the total effective dosage model to appropriately scale his results with the intensity
of his equipment, he shortens his trial time.
Dtotal(t) = 11fmxEo,(A, t) (1 - 10-A(A,I) )<b)(A) dA dt
f0
(3.3)
JAmin
Martin defines in [35] Amin and Ama, as the minimum and maximum photolytically
effective wavelengths (units: nm), A(A,t)as the absorbance of the sample at specified
UV-visible wavelength and at time t, (units: dimensionless), Eo(A, t) as the incident
spectral UV-visible radiation dose to which the polymeric material is exposed to
at time t (units: J cm- 2 ) and <O(A) as the spectral quantum yield, the damage at
wavelength A relative to a reference wavelength (dimensionless).
The total effective dosage,Dtt,, is defined contradictorily as both the total number of absorbed photons that contribute to the photodegradation of a material during
an exposure period and as having units of Joules. This in addition to Eq. 3.3 being
dimensionally inconsistent with either definition leads us to define our own model
closely related to the one put forward by Martin et al.
EA
Areas
j=
I
In our model, Eq. (3.4),
J
Iri(A, t)(1 - 10A(A))<b(A)dt dA
(3.4)
Amin
A
is the energy absorbed by the sample per unit area
and we include Iri, the spectral irradiance hitting the sample in
cm 2w
, instead of
the radiation dose E0 . We will also expand this model to find the total number
of absorbed photons. Because the Martin's definition is different than the one we
propose, we spend the next chapter deriving the proposed model and accompanying
metric.
Similar work employing dosage models has been successfully applied in photometry, radiometry, and nuclear science. A table of the units (Fig. 3-2) is included to
define terms that may differ across fields. In this chapter we have suggested that the
field is in need of a characterization for the stimuli of photorheological fluids and have
suggested that a dosage metric founded on the absorption of light might be relevant.
SI Unit
Meaning
IUnit
Einstein
Radiant Energy
Radiant Power
Radiant Intensity
Moles of Photons
Energy
Energy per time
# Einsteins
Radiant Energy
Radiant Power (Spectrum)
^-
Notes
Joules (J)
Watts (W).. ........
------ ............
.....
....
(Spectral) Radiance
Figure 3-2: The study of light is at the heart of many disciplines including radiometry,
astronomy, and spectrometry. This chart summarizes the definitions used in this
document.
Chapter 4
Quantifying Photon Delivery in a
Photochemical Reaction
In the following chapter we derive from first principles how measurable properties of
a reaction (in the most general case, the concentration of a reactant of a reactant)
are related to the photon source. As a result of our derivation we see that we can
predict how our reaction will vary over a range of experimental conditions including
the lamp irradiance, the initial concentration, and material properties.
4.1
Monochromatic Source
Let us return to the experimental embodiment of the Beer-Lambert Law which relates
two measurable properties, radiant intensity and transmitted radiant intensity, to the
absorbance or optical density of a sample:
A =lo1io.
(4.1)
ItA
The radiant intensity, IA, is incident on the surface from a monochromatic beam of
wavelength A, It is the radiant intensity of a monochromatic beam of wavelength
A transmitted through the sample, and AX is the absorbance for a particular wavelength under experimental conditions. In most disciplines, the logarithm in the Beer-
Lambert law is base e. However in chemistry, for liquids and solids it is common
to use base 10, which we adopt here. The absorbance is a combination of material
properties, composition of the sample, and experimental parameters as previously
discussed and is defined as
A, = e'l[ S].
(4.2)
Here eA is the molar absorptivity for a particular wavelength of the material, [S] is
the concentration of the absorbing species, and 1 is the thickness of the sample.
Barring reflectance, we can rewrite Eq. (4.1) as a statement of energy conversion,
lA - ItA = laA.
(4.3)
The radiant intensity of a monochromatic beam of wavelength A absorbed by the
sample is aA . While the incident and transmitted radiant intensities can be measured,
the chemical reaction is related to the number of photons absorbed. This quantitative
is captured by the absorbed radiant intensity given by Eq. (4.3).
We can solve for the ratio of absorbed radiant intensity to incident radiant intensity if we know the absorbance corresponding to our experimental setup. The
absorbance of a sample is often measured by a UV-Vis spectrometer, which measures
the absorbance through the Beer-lambert law. Combining Eq.(4.1) and Eq.(4.3), we
find
I"A =
1-
10-
(4.4)
If the sample thickness is small and the solid angle of the beam is small we can assume
that the areas defined by the beam before and after the sample are approximately
equal. This allows us to write the ratio of radiant intensities in Eq. (4.4) as a ratio
of irradiances:
IrA
IriA
= 1
-
10-^_,
(4.5)
if 1 < 21
(4.6)
Areaj
The solid angle describing the beam is Q; the incident area defined by the beam's cross
sectional area on an incident surface is Areaj; IrjA is the irradiance of a monochromatic beam of wavelength A incident on a surface; IraA is the effective absorbed
irradiance or the power of the beam absorbed by the sample over Areaj. If we can
measure Ira.\ and can assume that the energy is uniformly distributed across the
beam, then we can infer the predicted number of photons the material is absorbing
per second from the differential equation:
dNaA = IriA(1
-
.
10-^A)Areaj
hc*
dt
(4.7)
Here d dt is the predicted number of photons per second of wavelength A the material
will absorb, h is Planck's constant, and c is the speed of light.
For an experiment of duration T, we can now predict the energy delivered which
is absorbed per unit area for a monochromatic beam of a known wavelength
EaA
Areaj
_
Jo
Ir a(1
-
10-^^)dt.
(4.8)
This is related to the number of photons per area delivered during this time
S=
Areaj
i
IriA(1
-
10
-A ^)-dt.
hc
(4.9)
The quantum efficiency is the probability that a molecule undergoes a chemically
significant change after absorbing a photon of a particular wavelength. With this, we
can modify our metric to predict the number of molecules that will undergo chemically
significant transitions after absorbing photons from a polychromatic beam:
NmA
Area,
f Ir A(1 - 10-AA )<
A dt,
o
hc
(4.10)
where NmnA is the number of molecules affected by a beam of monochromatic light,
and <b(A) is the quantum efficiency. This means that we can predict the relevant
concentrations of the affected molecules in our sample using
[S]
(4.11)
[SO] - Nm
N AV
Nm
[S'] =[S'] +
.
(4.12)
Here [So] is the original molar concentration of the untransitioned molecule, [SO] is
the original molar concentration of the transitioned molecule, [S] is the new molar
concentration of the untransitioned molecule, and [S'] is the new molar concentration
of the transitioned molecule. The number of molecules transitioned is converted to a
concentration by using Avagadro's Number, NA, and the sample volume, V.
4.2
Polychromatic Light
To expand the monochromatic form to polychromatic light sources we need to address
whether contributions from individual wavelengths are independent and additive.
The "Addition Theorem" [47] requires that for a given effect which may be produced
independently by several specific wavelengths of light, an equal effect can be produced
by the combination of several of these wavelengths. Deviations from this theorem due
to secondary photoreactions and photorecovery, are beyond the scope of this thesis
and will not be addressed here.
We consider a polychromatic source to be a collection of monochromatic sources.
Each of these monochromatic sources is a slice of a polychromatic source over a small
wavelength range
Ira,= Ir(A)A A.
(4.13)
Note that photons are discrete entities with a continuously varying characteristic.
The Addition Theorem supposes that the number of molecules transitioned is equal
to the sum of the number of molecules transitioned due to each wavelength
Nm
f
(4.14)
NmA.
(=aIrA)
By subsitituting Eq. (4.13) and Eq. (4.14) into Eq. (4.10) we find:
Nm
A
,
Iri(A)(1 -
10A(A))<b(A)
dt
A A.
(4.15)
(Jco=~i
Areaj
Which in the limit of infinitessimaly small AA becomes,
m
Iri(A)(1 - 10-A(A))<b(A)--dt
=
Areai
Amin
(4.16)
dA.
hc
0
Note that Iri(A, t) is the spectral irradiance and has units of
Wn.
This expres-
sion captures the fact that both the molar absorptivity of a material and the radiant
intensity, and therefore the irradiance delivered by a lamp (often called spectral irradiance), is wavelength dependent.
As chemists are ultimately interested in the
number of photons absorbed, we are not concerned with the difference between a 365
nm photon and a 366 nm photon if both are absorbed.
4.3
Time Dependence of Terms
In the previous section, we assumed that the terms were independent of time. However, the concentration of the absorbing molecules may be changing, as well as the
molar absorptivity and quantum efficiency if a new species is introduced upon transition. In addition, mercury lamps are known to have a large power degradation and
a subtle spectrum shift over time. This time dependence can be accounted for by
modifying Eqs. (4.8) - (4.10) as
EA
_
Iax I
]a11a
Area
Amin
Iri(A, t)(1 - 10-E(At)[S](t)l)dt dA
(4.17)
IrJr(A, t) (1 -lO0E(At)[S1(t)) A dt dA
hc
Jo
(4.18)
Nm
Area
max
1
A
fT
Areas
ohcIr(A, t)(1
--
10
.1,
(
t)[s](t)1)<b(A, t)
dt dA.
-A
(4.19)
Finally by taking a time derivative of Eq. (4.19) and rearranging, we find the integrodifferential form of our polychromatic evolution equation:
d[S]
A-,
fAmax
-=Iri(A,t)(1
dt
NAV
-
A
10 -<(A~t)lsI(t))(A t)-dA.
hc
Amin
(4.20)
For compactness Area has been shortened to Aj.
4.3.1
Limiting Case: Time Independence
Let us consider first the case in which all of the quantities are time independent.
This reduces Eq. (4.19) to a statement equivalent to an experimental observation
termed the reciprocity law. For a given photoresponse, a material is said to follow
the reciprocity law if the material response is constant with the product of irradiance multiplied by time [11]. If the material response is linear with the number of
transitioned molecules, then the following equation is a statement of reciprocity:
Nm
Area
r
Iri(A)(1 - 10-E(A)[s]l(A)-dA
Amin
N
Nm
Are
(4.21)
hc
K f(A)(4.22)
(4.23)
where K is a constant for a given experimental setup and scales linearly with the
irradiance of the source. This model suggests that the rate of photon delivery does
not matter, but rather the absolute number of photons delivered. The reciprocity
law most applies when there is the "right amount" of photons to molecules. If there
are too few photons (much less than the number of absorbing molecules), we expect
our absorbed energy to be an overestimate of reality as the photons could miss the
few absorbers in space or some degradation process could prevent us from measuring
a bulk response. On the other hand, if we flood the sample with a large number
of photons then the material response should no longer be linear with time because
it has reached an upper limit. These two cases, illustrated in Fig (4-1), bound the
application of the reciprocity law.
Some materials deviate from the reciprocity law, and are labeled as demonstrating
reciprocity law failure [361. For reference, Schawrzschild modified the reciprocity law
by introducing the "Schawrzschild coefficient", p, which describes some reciprocity
law failure responses: applicable to some materials.
Constant = T Ir.
(4.24)
These failures most often happen at either very low or very high irradiance levels.
This could be explained by the limits previously described. Reciprocity law failure
also has been observed with photographic materials where there are many absorbing
reactions and a many step developing process. Metrics excluding the multi-step and
time dependent reactions present may not be appropriate for these applications.
4.3.2
Limiting Case: Time Dependence
Where previous polymer degradation studies are not concerned with the absorbance
changing with time (and therefore make the time independent approximation), our
photoactive systems may change dramatically over time.
For instance, an entire
concentration of the absorbing species could permanently transition to some other
non-absorbing state. This means that our metric at this point will become zero because the concentration, [S], is zero. This represents a large change over finite time.
In another case, the photoactive species could transition between two states that
have different absorption spectra and therefore absorb photons with a very different
wavelength than initially. Past methodologies include using a negative quantum efficiency to represent the competing process called photorecovery [341, [28]. The use
of a negative quantum efficiency is physically dubious. There may be better ways
to account for competing reactions and large changes in the absorbance spectrum
stemming from the introduction of a new species competing for photons. To do this,
we explore reaction kinetics in the next chapter
z
Z"040
N
I r
S
Figure 4-1: Regimes of application of the reciprocity law, with the number of converted molecules due to absorption on the y-axis and the number of photons delivered
on the x-axis. Reciprocity failure is expected when there is either a small or large
photon flux.
Chapter 5
Kinetics and Large Changes with
Time
We wish to examine the rates of our reactions even when the original species concentration may become significantly depleted. Over the course of this chapter we use the
differential form of the model we have developed to formulate a way to theoretically
analyze rates of reactions whose limiting timescale is photon delivery. In practice,
rate laws are empirical and experimental data is required to validate a particular rate
law. Therefore we will compare literature data and, in a following chapter, our own
data to our prediction.
In the first part of this chapter, we examine fluids whose
transitioned state does not absorb photons and therefore cannot return to its original
state, leading to an irreversible transition. For fluids whose second species has an
absorption spectrum that is larger than that of the original species, the transition
may be reversible, especially if the emission spectrum is tuned to favor one species or
the other (such as [54],[46]). In the second half of this chapter, we will address these
reversible fluids. For both types of fluids, we examine the effect of monochromatic
and polychromatic light.
5.1
Development of Kinetics within a Theoretical
Framework
To construct the simplest rate law, we first examine the case where [S'] does not
absorb photons and the reaction is irreversible:
S
S*
Kdgs S'.(51
Krs
-- +
(5.1)
Eq. (5.1) describes how the species S can become S' through the activated state
of S*. The fact that not all S* become S' is reflected in a quantum efficiency that is
not 1. If the quantum efficiency were 1, Krs would be zero. The relationship between
the rate constants and the quantum yield is given by
Kds
.d
Krs + Kds
4s =
5.1.1
(5.2)
Approximations
Historically, a number of estimates for the rate constant for the S to S* transition
have been used ([59], [16], [62]). Zimmerman et al. [62] suggests, for instance, that
the rate constant be taken as the rate of light absorption of each isomerization. Other
chemists, such as in [16], suggest
d[S]
dt =-
'
-K[S]csAIrA
(5.3)
where K is a constant, Es, is the molar absorption for the species S at a particular
wave length, and IrA is the irradiance of the wavelength in question.
Our model can be used to determine whether a zeroth order rate equation is
appropriate and how this rate constant might be defined. We begin with the full
polychromatic derivative with the concentration [S] explicitly written as
A
d[S]
=S- NA
dt
NAV
<=A
--- Iri (A)(1 - 10-E(A)1ls])-I(A)dA.
hc
Amna
(5.4)
For a laser, i.e. a source with a dirac delta in spectral irradiance, this reduces to
d[S}
dtdt
1 AAIriA(1
A
-
NAV hc
-
i
10-E's1)(A).
(5.5)
If we make the approximation that the absorbance, e(A)l[S] in Eq. (5.4), is large then
the rate equation reduces to a zeroth order rate law Eq. (5.6).
d[S]
dt
A
-
NAV
A (A)
hc
(5.6)
Note how this reduces to Eq. (5.7) matching the currently accepted rate law and
elaborating on the makeup of the constant in Eq. (5.3)
d[S] =S -a = -CGMIraAA4(A).
dt
__
(5.7)
Here C represents fundamental constants, G represents geometrical constants and M
represents material constants. From Eq. (5.6), C equals N
ch,
G equals -, and M
equals N(A). We see that the source influences the rate of reaction both with irradiance and wavelength. For example two lasers with the same power but different
wavelengths cause different rates of transformation from S to S'. The experimental
manifestation of Beer's law suggests that this wavelength dependence is not a rate
associated with the speed of absorption, but rather that the molar absorptivity captures an 'absorption efficiency' as a larger population of molecules is activated for a
given number of photons. This efficiency is separate from a quantum efficiency and
may be more recognizable if rewritten as the absorption cross section (o) which is a
measure of the probability of the absorption process,
o = 2.303
E = 3.82 x
NA
10- 2 1 E.
(5.8)
When the concentration or absorbance becomes too small, the linear approximation
is no longer valid.
if
1 0 -l)s]
~ 1,
(5.9)
then we replace the exponential term with a first order Taylor Series approximation
within the series' radius of convergence. This leads to the first order rate law
d[S]
A Irj.\lrs1A[A
NAV
hc
dt
(5.10)
In the next section we will find that while these approximations are not necessary
for the monochromatic source which has an explicit solution, they provide a solution
pathway for more difficult problems like reversible fluids and polychromatic light
sources.
5.1.2
Nondimensionalization of Monochromatic Case
Now that we have explored intuitively the rate of transition between S and S', we
nondimensionalize Eq. (5.5) and evaluate it directly. We assume <D = 1, though it is
easily re-inserted if desired. We define a nondimensional concentration [S] which is
the familiar quantity known as the absorbance introduced earlier,
[SI = e,[S]l.
(5.11)
Employing this definition, leads to the partially nondimentionalized equation:
d[S]
=
A
NAV
-
A
)TAh
(1 - 10[).
(5.12)
Note that the expression ^V is defined as unity. We must now nondimentionalize
time by a relevant experimental time scale. An appropriate nondimensionalization is
suggested by grouping the remaining terms in Eq. (5.12):
hc NA
(5.13)
We now can rewrite the fully nondimensionalized rate equation:
d[S
di
-(1
-
10[).
(5.14)
Nondimensional Groups for Monochromatic Source Case
The two dimensionless numbers, [5] and t, provide insight into the two factors that
affect the rate at which the reaction progresses. [] represents the number of "perfect
absorbers" in the solution as it describes both how many absorbers are in an area, [S]l,
and how efficiently they absorb, c. The larger this number the longer [S] decreases at
a constant rate. The time axis is scaled to reflect the fraction of the reaction that has
taken place. If t is larger the reaction is closer to completion if it is smaller it is farther
from completion. This is because t is directly related to the reaction coordinate: the
longer (large tep) batches of photons (large IrAA) are delivered to molecules that
efficiently absorb them (large C), the more molecules that transition.
Characteristic Curve for Monochromatic Source Case
The nondimensional rate equation is a separable equation, and can be integrated by
substitution yielding,
[$] = logio ((10I
- 1)10-i +
)
.
(5.15)
Here [S]o indicates the initial condition and t the scaled experimental timescale. Even
though this equation is nondimensionalized, the dependent and independent variables
are not normalized to 1. In fact, this equation represents a collection of curves as
the solution depends on the initial concentration as shown in Fig. 5-1. Note that the
zeroth order and first order approximations made in the previous section are captured
by the characteristic curves. The solution may indeed be considered linear in t until
logio(10so
- 1), when the linear solution predicts total conversion prematurely.
If we perform a variable substitution that collects both the initial absorbance
(EA[So]l) and the time varying concentration into a single variable, we can collapse
10
8
6
<CD
4
2
00
2
4
8
6
10
12
14
A
t
Figure 5-1: The evolution of S with j upon monochromatic irradiance depends on
initial concentration $o. For small t, $ is decreasing linearly with i, and for large i it
decreases exponentially.
100
102
<N
10-
10 -
108
10-10
0
2
4
10
8
6
Figure 5-2: Evolution of Z with t upon monochromatic irradiance describes behavior
of modeled photorheological fluids. The family of curves of S vs t seen in Fig. 5-1
collapse onto a single exponential curve.
this family of curves onto a single curve (Fig. 5-2). Let
Z
=
[-i
and substitute
Z into Eq. (5.14). Solving leads to the single curve:
Z=10--.
5.1.3
(5.16)
Validation through Analysis of Existing Literature
There is evidence that light reactions do have these types of characteristic shapes
and evolutions.
Early interest in the time evolution of photoresponsive materials
originated in the photography and astronomy fields [58],[25],[27].
However the data
required to generate the characteristic curve is often not reported. To normalize the
data as suggested above, one needs not only molar absorptivity, wavelength of light,
initial concentration (all routinely reported) but also the thickness of a given sample
and the absolute irradiance of the light source at the sample. Some experimentalists
1.0
0.8
all
0.4
0.6 -0.
0.07_
0.1
0.01
<N 0.4
A
C21
S1/3
0.2- .*
1
A 10
t
100
100
t
.
c2
I10C2
0
0I
0
0
-L
0.01
04
,
0.1
10
1
100
1000
A
t
Figure 5-3: The metric is applied to the dataset [62] with a slight modification in the
intensity (Io = AIm). This is equivalent to <bA=313nm = - as the quantum efficiency
also linearly scales the intensity. The black line is the theoretical prediction The inset
shows the Z vs t using the original parameters. See Table 5.1
only report relative intensities within an experiment while others are more careful to
report absolute intensity in terms of photon fluxes.
To demonstrate the validity and usefulness of the above nondimensionalization, we
will examine a dataset that reports most of the required quantities. This particular
dataset reports measurements of azobenzene, a compound that is well documented
through out literature. We have examined other published systems such as iodine
in retinol ([3]), azobenzene in a polycarbonate film ([38]), and photoactivated CdSe
nanocrystals ([40]), and found similar behavior, however since many of the required
variables are unknown or unreported, we deem the analysis less convincing and proceed with the present case. Zimmerman et al. [62] report a time evolution study of
several different concentrations of trans-isomer azobenzene irradiated at different intensities of monochromatic light. They also report the photostationary mole fraction,
the ratio of converted isomer to original concentration, as a function of wavelength.
Using their reported experimental conditions, listed in Table 5.1, we nondimensionalize their data using the proposed scalings for Z* and t* values. Note that the area
Table 5.1: Experimental parameters from Zimmerman et al. [62]
Concentration (-4)
Im
C1 = 10~5
5
c2 = 2.5 x 10~
c2 = 2.5 x 10- 5
C2 = 2.5 x 10-5
C3 = 10-4
C4 = 10-3
Intensity (mW)
=
1m =
Im =
Im =
1m =
Im =
2.99
3.03
0.91
0.30
3.02
3.81
1 = 1.25cm A = 5cm 2
A = 313nm E = 10"m L
A, 1 approximated from reported V = 6.204cm 3
and the thickness of the sample is not reported and we approximate these under the
assumption that the sample is a cylinder of equal dimensions in radius and height. We
then use this area to calcualte the irradiance from the measured intensity (originally
reported in einsteins per minute).
In the inset of Fig. 5-3 we see that the nondimensionalization of the data does
indeed cause the data to collapse onto a single curve. This is a strong indication that
the nondimensionalization correctly accounts for varying concentrations, varying irradiations of light, and time dependence. When we compare this to the expected
characteristic curve however, we see that the results are shifted by an order of magnitude in.
Upon examining the definition of t, we see the only opportunities for
moving the data onto the prediction are in texp, and IrA. Since the experiment was
conducted over a time scale of minutes, it is unlikely an order of magnitude error was
introduced in the time measurement. The irradiance however is a derived quantity
from the given intensity measurement. We find that if we diminish the irradiance by
a factor of ten, the data now lines up with the theoretical prediction (Fig. 5-3).
While relative intensity was determined in an experimentally rigorous way, the
absolute intensity remains questionable. This difference between relative and absolute is consistent with the fact that the data points collapse on each other but not on
the theoretically predicted curve. The absolute intensity was determined by the au-
thors using uranyl oxalate actinometry, a separate chemical reaction. Any difference
between the two experiments, e.g. path length, or transmission of the quartz, would
skew the irradiance values.
Also, in our metric we assumed a quantum efficiency
of 1. While the quantum efficiency is controversial and has been defined differently
over the years, the azobenzene paper defines it as .44 at the indicated wavelength.
A further reduction in intensity of .2 could easily occur particularly given that the
light source was uncollimated and that intensity drops off as an inverse square law,
making it particularly sensitive to small changes in path length. Also with such a
thick sample the intensity at the bottom of the sample could be considerably less than
the intensity at the top of the sample leading to a lower effective intensity. Lastly,
the irradiance was calculated by dividing the intensity over the approximated area.
If the area is larger than the 5 cm 2 assumed, the irradiance would be smaller. Of
course, changing the area would also change the sample thickness as the volume is
given. Nonetheless, we have shown that there exist reasonable values for A, 1 ,Io, and
<b which would shift the experimental curve to the left leading to agreement with the
theoretical prediction.
One may also question why the dataset follows the theory but then diverge beyond t =1. To understand this discrepancy, we move away from t and Z which are
somewhat unintuitive and can mask the evolution of the concentration. In Fig.5-4,
we see the molar fraction of the cis isomer rise with time. Our model predicts 100%
conversion which is not reflected in the data (the data predicts somewhere around
80%). An irreversible fluid assumes that the entire population is eventually converted.
In practice the cis isomer also absorbs and so can revert back to the trans-isomer. In
addition, the cis-isomer can thermally isomerize back to the trans-isomer. There are
a variety of approaches we can use to compare our predictions to the data despite
this complication. In Fig. 5-5 (a), we simply scale the previous theory to .8 to reflect
the observed photostationary mole fraction. In Fig. 5-5 (b), we try a more physically
motivated method. For each concentration, we determine what fraction of the population is not absorbing photons and subtract this from the initial concentration. We
then add that fraction of the population to the calculated concentration. This ap-
1.0
0.8
-
E
0
0.6
---
e.-
-
......
_03 C,
e'
0.2
0.
600
c2
*
-
-
-
|10
*.--
*
0
..--
1200
1800
Time(s)
2400
3000
3600
Figure 5-4: Theory over predicts the final photostationary mole fraction as it neglects absorption of Cis-Isomer and requisite Cis-trans isomerization. Points indicate
experimental data [62]; lines are theoretical predictions.
proach, while better than the previous, is still chemically dubious. More appropriate
corrections will be discusses in a later section, in which we develop a monochromatic
solution for chemically reversible fluids.
At this point we have discussed a rather idealized case, where the source is
monochromatic and the transitioned state has an absorption of zero.
We briefly
discuss an alternative approach in the next sections.
5.2
Extending Solutions to Polychromatic Light
Although the polychromatic form is the same as the monochromatic form with an additional integration over the wavelength, a closed form solution is no longer apparent
for the differential equation. To demonstrate this we rewrite Eq. (5.4) as:
dS]
dt
Amax
ZImin
f(A)dA +
[(f)(A)10-[s()dA
J~min
(5.17)
1.0
0.8
0.6
0.4
0.2
0.0
0
600
1200
1800 2400
Time(s)
1200
1800
Time(s)
3600
3000
1.0
0.8
0.6
0.4
0.2
0.01 '
0
'
600
'
I
.
2400
1
3000
U4
3600
Figure 5-5: Comparison of experimental data [62] with two theoretical formulations.
a) The monochromatic solution is simply scaled to 80% of original value. b) The
initial concentration is modified to reflect the population which will not be converted.
We assume that researchers could evaluate both of the functions f(A) = A
Iri(A)L
and g(A) = e(A)l. Attempts to nondimensionalize this equation are thwarted by the
fact that we cannot separate S from g(A) in the second integral. Because of this, the
concentration evolution from a polychromatic source must be integrated numerically
for an exact form. However, we can develop two approximate solutions: a linear
solution appropriate for large absorbances and at short times, and a nonlinear solution
comparable to the monochromatic solution for small absorbances.
First, because of its definite limits, the first integral is simply a constant
fma f(A)dA
K =-
(5.18)
where
K>
fXmax
f(A)(10-[s)9(A)dA.
(5.19)
At short times, the polychromatic form of the rate equation reduces to a zero-order
system, linear with K; this is the short time polychromatic form of Eq. (5.6) .
Employing the initial concentration So to nondimensionalize S, we find that short
time solution can be approximated as Eq. (5.20) with dimensionless groups given by
Eq. (5.21), and Eq. (5.22)
S= -t' + 1
S'
t'
NAchVSo
.
=
so
J=.Ir(A)AdA.
(5.20)
(5.21)
(5.22)
Amin
Next we can evaluate at what concentration this assumption is no longer valid. First
we define C as
A
C
=
"a" f (A) (10-[s])9(x)dA
"m"in f()(moasx)f(A)dA
ff"""
f(A)dA\
(5.23)
If C > 1 the linear assumption is not appropriate and the full solution should be
calculated numerically. During a one second interval, the linear approximation is
within 1% of the exact solution for absorbance functions larger than 5.
If the maximum absorbance is
Next we consider the small absorbance limit.
small (emal[So] < .2) we can take the first two terms of the Taylor series expansion
for
1 0 -E[S]A
~1 - ln(1O)E(A)l[S] +
} (ln(1O)E(A)1) 2 [S] 2 ,
and integrate the differential
equation to get an analytical solution
5
=
1
-
(5.24)
3SO(1 - 10)(
ln(1)lSo f-" Ir(A)A(A) 2 dA
2So _
2
fAax Ir(A)Ac(A)dA
S =-
=
;
()
j
(5.26)
so
Ir(A)E(A)AdA.
(5.27)
Note that this solution has a singularity followed by nonsensical results if /2 > '31.
This is to be expected when the two-term Taylor series is no longer sufficient.
The solutions to the monochromatic solution and polychromatic solution (large
and small absorbance) are presented in Table 7.1. The approximations serve mostly
to provide suggestions for relevant nondimensional groups that can be used to characterize an experimental set up. Note that the dimensional groups for t all look
Table 5.2: Dimensionless groups and solutions for irreversible fluids irradiated with a
monochromatic source (1), a polychromatic source for a fluid in the large absorbance
regime (2 a) and in the small absorbance regime (2 b)
1
[5]
logio ((10o]O - I) 1 0 i + 1)
S
2(a):
2(b):
S
Solution
Case
5
[5] =A[Sl
-ti+IS
=
1-1
3SgI-
-0i
2a
5
=
l
tex
I
VSo Na
texp
so7
A
NA
Amax
IAm~
he
Amin
Ir(A)AdA
hc
Ir(A)e(A) A dA
NA
he
similar to each other. In fact, t reduces to t for monochromatic sources and the two
are related to each other by a constant. It is understandable that case 2(a) looks
slightly different, missing the molar absorptivity and the length scale, because in this
regime the fluid is not limited by the absorption of the fluid but by the delivery of
photons. From this table we can see that a good recommendation for our metric is
therefore the 2(b) case, i. However, for large absorbances and short times, t' may also
be an acceptable choice. Nonetheless, to describe an experiment we recommend that
researchers report the following minimum variables, c(A), Ir(A), V, A, So, so that they
or another author can normalize the time scale. We have yet to find literature that
appropriately reports experiments performed with a polychromatic source (though
[11] may be considered a notable exception), therefore chapter 7, which describes our
own experimental data, is in part used to validate this section.
5.3
Reversible Fluids
We have already encountered a fluid that requires us to extend slightly our theory to
fluids which have two states that absorb UV light:
B
(5.28)
'- B* +A.
(5.29)
A N A*
KrA
B
KrB
We call this a reversible fluid and the bulk E and <D change in a way that is not
obviously related to the time dependent concentration. Some trans-cis isomerizations
are good examples of systems in which the when the resultant species ([B]) competes
for photons with the original species ([A]). For the time being we will assume that
all A* become B and all B* become A indicating a quantum efficiency of 1 for both
reactions. This assumption need not be made and <D may be added back into the
formulation in addition to the reaction associated with Kd,.
Since our robotic application has a preference for reversible mechanisms we seek
to formulate a rough prediction of the behavior of these fluids. This rough sketch is
essential for understanding the feasibility of controlling a material property based on
turning on and off different wavelengths of light. We will begin as before, first with
the much simpler monochromatic case and then expanding the analysis to show that
once again reporting the spectra is essential to predicting the photostationary state.
5.3.1
Monochromatic Case
The rate of generation of the two species must be related to the concentrations of the
two species absorbing photons. We assume these reactions are independent of each
other:
d[A]
dt
-
d[B] =
dt
fa([A])+
|fb([B])|
(5.30)
fb([B])| + Ifa([A])I
(5.31)
We also assume that each of these functions are well described by our previous discussion:
d[A]
dit
_
Areaj IrA(1
-
1 0 -AI[A
-
1+
10 -EI[BI),
NAVhc
(5.32)
for example. We consider the case in which initially there is only one species present
so that we can relate the second species to the current concentration and the concentration of the first,
[B] = [Ao] - [A].
(5.33)
Note that Eq. (5.32) and Eq. (5.32) are sufficient to generate a numerical analysis. We
proceed with determining analytical approximations to gain insight into our model's
application to reversible fluids. Using a first order Taylor series approximations for
10
~AI[A1 and
1 0 EB[A]
(requiring EAl[A] < 1 and eB[A]l < 1 ) on the combination of
Eq. (5.32), and Eq. (5.33), we can write the differential equation for the concentration
evolution of A (Eq. 5.34) as:
d[A -
" rNatlA((Ko - 1) + (CA + KOeB)1n(10)1[A])
(5.34)
where
K
o -
1 0
(5.35)
-B^[Ao]
The quantity Ko is defined for convenience and to emphasize at this point that no
requirements on the magnitude of KO have been made.
After applying appropriate initial conditions, integrating Eq. (5.34) and solving
for A, we find:
[A)]=
[A0]10-t(NAra
(KO
IrxA(EA+B*K)
[ A)
=
[A]-
1
)[ 1 0
(CA
^+Bo)
+ EBKo)lfn(O1)l
.
-
(5.36)
1 - ln(10)EBAol + O(ln(1O)eBAol)2 we find
Approximating K as Taylor series KO
--A C EB
[A] = ([AC.
-
O
I.AE+B
_tAroa
)
NAO)
10B
0
- E2ln(10)0
-t NArc
UAr\(EA+En-n(10)E2
B
A+
±
EB -
[Aol
(5.37)
l(10)[Ao]l
E
(5.38)
CB
Defining dimensionless groups:
[A:=(1 -
CA
+
CR -
CB
6l4ln100l}
~
10-1+
1
CA + EB - C2 l(10)[Ao]l
Areal
4Ir(EA +e B - lin(10)41[Ao]) A
-texp
V
NA
hc
[A]
[A]
[A0 ]
(5.39)
(5.40)
Note that Eq. (5.38) implies a similar form as the monochromatic form but decreasing
at a slightly slower rate and implies a photostationary mole fraction dictated by a
function involving the ratios of the two species' molar absorptivities. As the first order
Taylor series approximations are not sufficient to fully describe the power series, we
are not surprised by the singularities apparent in the denominators.
We have applied this to the azobenzene data discussed previously. The cis-isomer
molar absorptivity (1000
mo1L cm)
from the NIST webbook (11300
is reported in [62] as an order of magnitude different
moiL cm)
[53]. Therefore we have a large fitting range
1.0
0 .8 -........
..........
.
E
00.61
Co
c0.40
--
-
0.2
0.0---
0
600
_
PIf0
...
.... C3
1200
C2-
a
_A__lcc
1800
Time(s)
Figure 5-6: The reversible fluid monochromatic formulation is applied. Note that the
Io = 1/20Im, and eb is 103.m eMwe could use. Fig. 5-6 uses a molar absorptivity of 5012
mL cm.
Again, we must
modify the intensity to be 1/20th of the reported intensity. Alternatively, we also find
promising agreement with the data if we modify the thickness of the sample to be 1.5
mm and the area to 41 cm 2 (approximately a 3.6 cm radius) and use the reported
quantum efficiency of .41.
We can also use this to determine the photostationary mole fraction:
EB(5.41)
EA +
EB -
E62 l(10(
This data is easy to collect and the aforementioned paper also reports the standing
concentration. We can compare our prediction with their results as another check
(See Table 5.3). The calculation used to generate this prediction uses only the reported experimental parameters and accepted physical constants. Our predicted mole
fraction has not included the thermal isomerization of the cis-isomer to trans-isomer.
Therefore the over-prediction is expected. The large disagreement for the 254 nm
Table 5.3: Comparison of experimentally observed [62], and predicted cis-isomer photostationary states
A Predicted Mole Fraction Observed Mole Fraction
8%
80%
254
81%
96%
313
40%
72%
365
15%
26%
405
14%
28%
436
18%
28%
546
5%
16%
578
[Ao] = 2.5 x 10-
5
M
wavelength may be related to the large molar absorptivity of the cis-isomer at that
wavelength and the possible break down of the Taylor series approximation. This
data as well as the 405 nm data should be analyzed numerically. In general, we see
these results as being a satisfactory validation of our rough sketch.
5.3.2
Polychromatic Light Affects Photostationary State
Current wisdom in the chemistry community is that the standing concentration of a
photoactive material is independent of the power spectrum delivered [16]. Eq. (5.41)
supports this. In fact, there are four cases when the spectral power of the light source
is not relevant to the standing concentration:
1. [B] does not absorb photons (E does not change with time).
2. Light is monochromatic.
3. [A] and [B] have the same absorption and quantum efficiency spectrum.
4. Light has constant spectral intensity across all wavelengths absorbed by either
[A] or [B].
However, when [A] and [B] have different absorbance spectra and the light is polychromatic over relevant portions of the absorbance spectral, the spectral power of
the lamp can influence the final standing concentration. To begin, we can preform a
simple thought experiment. If a green light source is used to stimulate a mixture of
species where one absorbs green light and the other blue, the species absorbing green
will be most prevalent in the standing concentration. If however a blue light source
is used, the concentration will be dominated by the other species. To express this
mathematically, we can expand the monochromatic prediction to the polychromatic
case in the same way we did for irreversible fluids.
A =(
-
fA "a" Ir(A)AeBdA
"""
fJrnax
\
10-i +
ff;"Ir (A)A~dA )ff"
Ir(A)ACdA
(5.42)
"i
"- Ir (A)A~dA
(C= + EB - 6' ln(10)Aol)
(5.43)
The relevant dimensional groups are:
t
t
_ _
Amax
f
NAch JAmin
Ir(A)AgdA
(5.44)
A
A
=
A
(5.45)
Finally identifying the photostationary mole fraction is beneficial for comparison.
fmax Ir(A)AEBdA
#
M=""
(5.46)
fiMr" Ir(A)AgdA
A = (1 - #)10-- + #
This form is reminiscent of the procedure we applied to Fig. 5-5.
(5.47)
Note that the
photostationary concentration depends on the spectral irradiance.
In this chapter, we have developed approximations for the time evolution of concentrations for various situations including fluids stimulated by either monochromatic
or polychromatic sources, and fluids where one or both species absorb. In the following chapters, we will use the nondimensional groups that are common to these
solutions as a compact characterization for both experiments and lamp sources.
Chapter 6
Selection of Fluids
Having developed a framework to predict the speed of transition and power requirements of photoresponsive fluids, we select a few fluids to examine for application
in our robot and as case studies for our framework. In this chapter we introduce
three fluids, a micellar fluid, a nanoparticle fluid, and a hydrogel, which have various
combinations of advantageous properties. We briefly mention the mechanisms behind the change in rheological properties and their possible contributions as robotic
components.
6.1
Robotic Needs
Our robotic application requires a fluid that uses a low power commercial stimuli to
switch rapidly, preferably reversibly, between rheological states that permit or prohibit a mechanical function. Therefore an optimal fluid would involve a photoactive
ingredient with a high molar absorptivity of one state at one wavelength and another
also large molar absorptivity at another wavelength. Ideally, the two states would
require the transition of only a very small concentration of the photoactive ingredient
and would have a large physical change in rheological properties.
Our biggest restriction on the fluids we can test is the ease with which we can
synthesize them.
Since the population of photorheological fluids is small, this is
fairly limiting. We present three fluids that are synthesizable in the laboratory which
present different opportunities both for robotic application and scientific exploration.
The micellar fluid is a fluid that starts with a viscosity of approximately 10 Pa.s which
then decreases 1000 fold upon irradiation. The laponite fluid is a fluid that is easily
pumpable until it is irradiated and then develops a yield stress. Both of these fluids
represent one-way transitions and therefore are possibly appropriate for the active
slime for the robot. Neither of these would satisfy the ideal case for a mechanism
which is switchable. Therefore we include the reversible hydrogel as an example for
feasibility studies. While we did not do experiments with this material, we can make
some predictions that will help with understanding sizing of stimuli elements and
speed of reaction. With this in mind we introduce our materials.
6.2
Materials
New research in photoresponsive chemistry is producing simpler recipes for photorheological fluids. Now engineers can perform 'kitchen chemistry' that limits the complexity of synthesis making photorheological fluids more readily available. Ketner
et al. [30] addresses this and combines a cationic surfactant with a photoresponsive
organic acid to form a surfactant/micellar solution with viscosity tunable by light.
The same group has also developed a nanoparticle based light activated yield stress
material. Given that a marked increase in PR fluids is expected from these papers,
there is a need to coordinate stimuli descriptions for the purpose of comparing and
contrasting such fluids. To further the description put forward in the previous chapter, we conduct experiments on two of these systems: the micellar solution and the
laponite solution. For the purpose of our application we also discuss the possibility
of using a reversible hydrogel system. The following chapter gives specifics on how
each fluid works on a molecular level and how we prepared our materials for testing.
6.2.1
Photoresponsive Micellar Fluid
Ketner's photoresponsive micellar system combines cetyl trimethylammonium bromide (CTAB) with the photoresponsive molecule trans-ortho-methoxycinnamic acid
CTAB
CTAB
Aians
0.0
1.2
0
m l
22
aTtt
urs
V Light
tns-OMCA
T
(.
0.4.
[Lotas-nwormH
0240
280
320
s-OiCA
hr yidr
360
Wavelength (nm)
Long soa
Sh rt UIn=rr
Figure 6-1: A) The absorbance of 1mM of OMCA measured with a Varian Cary 50
spectrophotometer (thickness approximated as 1 mm) B) The viscosity change seen
after irradiation is hypothesized as being due to a change from long to short worm-like
micelles. These figures are reproduced from [301.
(OMCA). The absorbance of OMCA is shown in Fig. 6-1. Unirradiated CTAB/OMCA
mixtures form long wormlike micelles estimated as 3000 A in length. Upon irradiation
there is a dramatic reduction in the length of the micelles to less than 2% of their
original length, estimated now to be 40 A. This change is effected by the photoisomerization of OMCA which changes the relative energy for various worm geometries
and favors the formation of spherical endcaps over cylindrical body segments leading
to shorter micelles. Long worms tangle more easily than short worms and therefore
the bulk material has a higher viscosity. In this way the fluid changes from being a
highly viscoelastic fluid with a zero shear viscosity of approximately 10 Pa.s to a thin
water-like fluid with a viscosity < .01 Pa.s.
Preparation
OMCA was purchased from Sigma-Aldrich.
CTAB was purchased from Aldrich
Chemical Company. We used a magnetic stir bar and slight heat to aid the dissolution process. A 10M NaOH solution was used to neutralize the solution. Samples
were left to sit for at least a day before testing. The following procedure was used to
make suitable OMCA and CTAB solutions for testing.
1. Dissolve weighted amount of OMCA in de-ionized water
PAG
Bmen
odo/ Add benufn
Laponite
edgestu
+YeduetopH
drop
1.0
A
005
200
200
400
500 '
OO
700
800
Wavelength(nm)
PF127desorb
cmlapnile
PF127
micalles
with
odobe
nzneinside
Figure 6-2: a) The absorbance of 13mM PAG, 5% Laponite, 6% PF127 measured
with a Varian Cary 6000i spectrophotometer (thickness approximated as 1 cm) b)
The appearance of a yield stress is thought to be from the formation of a "house of
cards" network. Panel b is reproduced from [51]
2. Measure pH
3. Neutralize solution with NaOH
4. Dissolve weighted amount of CTAB in solution
5. Add NaOH till pH is between 9 and 11
Over the course of this research four batches of OMCA+CTAB solution were
tested. These batches are listed in Table 6.1.
Table 6.1: Composition of four batches of OMCA+CTAB solutions prepared for
experiments.
Label OMCA (mM) CTAB (mM) pH
A
50.1
59.8
10
B
50.3
60.3
9
C
49.9
60.4
11
D
50.0
82.8
11
6.2.2
Photoresponsive Nanoparticle Based System
We also briefly examine a nanoparticle photoresponsive fluid, [51]. This fluid holds
potential as it is very similar to previous slimes based on laponite. Pluronic F127
(PF127) sterically stabilizes dispersions of laponite when it is adsorbed onto the
particle faces. This discourages the formation of the "house of cards" network which
is thought to be responsible for the yield stress nature of laponite solutions. Upon
absorption of UV light the chosen photo acid generator (PAG), diphenyl-iodium-2carboxylate monohydrate, photolyzes into benzoic acid and iodobenzene. PF127 then
forms micelles around iodobenzene and the benzoic acid gives rise to a positive charge
on the laponite edges. The whole mixture gains a yield stress when a network forms
due to the interactions between the positive edges and negative faces.
Preparation
Laponite was acquired from Southern Clay Products, PF127 from Sigma Aldrich, and
PAG from TCI America. A 55 mL sample of 5% Laponite, 6% PF127, and 13mM
PAG were dissolved in deionized water. The procedure involved dissolving Laponite
into the water in mg amounts while being stirred with a magnetic stir bar and heated.
A vortex mixer was then used for over an hour to disperse the particles. PF127 was
then added and stirred. A large viscosity change was noted. Finally PAG was added
and the solution was stirred overnight.
6.2.3
Photoresponsive Hydrogel
We also include a photoresponsive hydrogel as a promising reversible candidate material.
The polymer chains of the hydrogel form an entangled network structure
via hydrophobic associations of C12 side chains (Fig. 6-3 (a)). The system has a
lower viscosity when a-cyclodextrin forms inclusion complexes with C12 side chains,
preventing these hydrophobic associations, shown in Figure 6-3 (b).
Because the
a-cyclodextrin preferentially attaches to the trans isomer of 4,4-azodibenzoic acid,
the hydrophobic associations can be blocked or unblocked depending on whether
azodibenzoic acid is in its cis or trans isomer.
Azodibenzoic acid (ADA) can be
isomerised by photoirradiation, resulting in a photoresponsive system
The material is termed reversible because we can irradiate the sample with wave-
Qfi
_UV
~~
visible light
Entangled
Less Entangled
Figure 6-3: A multicomponent system described in [54] is photoresponsive due to
a-cyclodextrin and the photoisomerizable azodibenzoic acid competing to bind with
'sticky' C12 sidechains on a poly-acrylic acid backbone
lengths less than 375 nm that will be absorbed by the trans-ADA, which then becomes
quasi-cis, or we can irradiate it with violet/blue light that will be absorbed by the
quasi-cis state which then becomes the trans isomer. This can be repeated a number
of times to switch between the two viscosity states as seen in Fig. 6-4 (b).
Synthesis
While ADA and cyclodextrin can be purchased commercially, the hydrogel must be
modified to include the C12 side chains. This is a simple synthesis procedure if the
lab is equipped with standard chemical equipment. We have synthesized this material
for future research. We have not done further experiments with this material due to
the need for good environmental controls (e.g. light isolation) during in situ testing.
0.61
0%
*4
0
0
e
trans ADA
e
quasi-cis ADA
0
0
0
*
0
0
0
0.4
*
0
0
0
0
0
- 000
I
I
I
I
I
0
0
0.2 ~00
S
0.
0
ee
*S
0.0'
25 0
-
-
300
350
400
450
500
550
Wavelength (nm)
10
UV
10w
s
UV
IuvVis
102
CL 101
*Nw
100
104
1
2
3
4
5
6
Times
Figure 6-4: a) UV-vis absorption spectra of 2.5 x 10-5 M ADA collected by a Shimadzu UV-2500PC spectrophotometer using a 1 cm path length quartz cuvette. b) A
ternary mixture of 5.0 g/L modified hydrogel, 10.0 g/L a-cyclodextrin, and 1.0 g/L
azodibenzoic acid experiencing repetitive irradiations with UV (closed) and visible
light (open) Both panels are reproduced from [54]
82
Chapter 7
Experiments and Polychromatic
Behavior
Our aim in this chapter is two fold. Firstly, we wish to provide validation of the
suitability of the material for robotics and secondly, to provide validation of the
theory for polychromatic illumination developed in Chapter 5.
7.1
Optical Hardware
As we have suggested that a method for characterizing our light source is an important
task, we begin by describing the UV lamp and related aspects of the experimental
setup. The light delivery system consists of two pieces; (i) the lamp and its accessories,
and the (ii)external hardware and optics, such as the UV rheometry fixture.
7.1.1
Experimental Setup
Light Source
There are many different applications utilizing UV light from forensics to sterilization.
It is not surprising, therefore to find a broad range of mercury or xenon light sources
on the market spanning UV lamps, LEDs, and lasers. All of these function in different
ways and produce different colored spectra. For our purposes, the most important
selection criteria besides emitting in the UVA range is repeatable irradiances at the
cure site. Not many lamps on the market allow intensity adjustments. Those that
do are intended to counteract the degradation of the lamp bulb that leads to increasingly dimmer outputs. Because of this, most of the intensity adjustment features are
manual and involve the user setting the output at a level that can be maintained
throughout the curing process. For our experiments, we selected a UV lamp that
features an automatic intensity adjustment feature, Fig. 7-1. The EXFO Omnicure
S2000 is a lamp with a high pressure 200 watt mercury vapor short arc bulb and
features "closed feedback technology" developed by EXFO. The EXFO lamp, with a
standard 320-500nm filter installation, delivers a spectrum of UVA (315-400nm) and
blue-green visible spectrum light detailed in Fig (7-2). This spectrum was collected
using the Institute for Soldier Nanotechnologys Ocean Optics USB2000 Fiber Optic
Spectrometer. The absolute spectral intensity was determined by calculating the area
of the relative spectral intensity (arbitrary units) and normalizing it to the measured
total irradiance.
The closed feedback technology of the EXFO Omnicure S2000 lamp was a key
reason for the selection of this lamp. Over the lifetime of a lamp, the bulb degrades,
notably 20% over the first 500 hours of use. To ameliorate this, the Omnicure S2000
has an adjustable iris that can be opened and closed to let more or less light through
to the waveguide. This operation does not change the relative spectrum of the emitted
light. This iris is controlled through a calibrated intensity sensor located close to the
bulb. The user can therefore set an intensity less than the current maximum output
and the output will remain within 2% of the commanded value. The entirety of the
tests reported here were performed within the first 50 hours of lamp use. This lamp
enables us to control the total irradiance present at the sample.
Waveguide
In conjunction with the S2000, we used a 5mm diameter liquid light guide (EXFO)
which is 1 meter in length and suitable for signals within the wavelength range between
250 to 600 nm. A difference in measured irradiance between a straight waveguide and
High Pressure 200 W
Hg Vapor Short Arc
Bulb
25
20
E
15
=
Data
M Variability -
10 5 -
0
0
20
40
60
80
100
% Iris Open
Figure 7-1: a) The EXFO S2000 lamp features a closed loop feedback system. A
calibrated intensity sensor monitors the total intensity exiting the lamp while an iris
opens and closes to produce the desired intensity. Panel adapted from [32]. b) We
demonstrate that the irradiance is linear with the percent of the iris that is open,
particularly at smaller desired irradiances.
0.20
0.15E
C 0.10-
E
0.05
2
2 W.cm-
0.00
100
200
300
400
500
600
700
k (nm)
Figure 7-2: Comparison of spectral irradiance between two different total irradiance
settings of the S2000 using the Ocean Optics USB2000 Fiber Optic Spectrometer.
Note that the spectrum does not shift between the two tests despite the difference in
total irradiance.
100
80 --S-10
100
Distanem
9
U~
LE
Endface
mm
5mm
mm
Ughtgue
Dae
6
6-mm
60
a
40
20
20
10
40
5
0
-5
Lateral Displacement (mm)
10
0
5
10
15
20
Distance from Lightguide Endface (mm)
Figure 7-3: Uncollimated light sources exhibit variation in relative irradiance both
across the cross-section of the beam (a) and along the path length (b). a) Illustrates
the variation across the cross-section of a beam from a 5 mm diameter waveguide.
b) Illustrates the variation in the peak irradiance from three waveguides with path
lengths greater than 2 cm. Figures recreated from data supplied by the S2000 manufacturer [33]
a bent waveguide was noted during operation. Therefore, all subsequent tests were
performed with the waveguide fully extended. The light emitted from the end of the
waveguide is assumed to be incoherent, uncollimated (diverging) light. If desired,
a collimator can be added to the end of the wave guide so that the emitted ray is
effectively a parallel beam and can be focused. The manufacturing specifications in
Fig 7-3 suggest that the energy of the beam is relatively evenly distributed across
its cross section 2cm away from the end plate. Collimating the light may have other
benefits such as lessening the peak irradiance decay shown in Fig 7-3 (b), but with a
trade-off in reduced overall irradiance. As the path length of the light from waveguide
to sample is larger than 2 cm, the experimental errors due to the lack of a collimator
are likely smaller than those introduced by the long path length (> 10 cm).
ARES UV Fixture and Other Hardware
Neither the lamp nor waveguide can be easily adapted to include filters and since
the intensity sensor of the lamp is calibrated with the manufacturer installed filter,
replacing the filter is not an option.1 A vertically adjustable stage (not pictured) is
'To test the wavelength dependence of the proposed theory one could use bandpass colored glass
filters to manipulate the spectral distribution of the beam. A filter wheel may be used in conjunction
with the described equipment to test the wavelength dependence of the above theory as shown in
irror
Bao
ss Filter
Quartz Plate
Cure-Site
Radiometer
Figure 7-4: The beam from the lamp travels from the waveguide through open air to
the ARES rheometer UV curing fixture where it is redirected by a mirror through a
quartz plate and to the sample. We use two radiometers to measure the irradiance:
one that measures the irradiance at the waveguide endface and one that measures the
irradiance of the beam at the cure site.
used to fine tune the alignment of the waveguide with the latter optics. The next
piece of equipment in the beam path is the ARES UV curing accessory. This fixture
is a cylindrical tube with a window through which the beam passes. The beam enters
the tube and hits a mirror placed at a 45 degree angle to the long axis of the cylinder.
The light then travels down the tube to a quartz plate 1cm thick. Quartz has a
transmission profile that has at least a 90% transmission in the range of UVA and
UVB so we can expect the the spectrum to be unaltered upon exiting the fixture.
The path length from endface of the waveguide to the mirror of the rheometer is
approximately 5 cm and from mirror to the end of the quartz plate 5.5 cm. After this
the material absorbs the beam according to the absorbance curves in Chapter 6.
7.1.2
Characterization
This detailed description of our optics should ideally collapse all this information into
a single metric. Ultimately, we wish to report the relevant nondimensional time for
the materials tested as discussed in a previous chapter. We make the approximation
Fig. 7-4. However in our setup the beam passes through the filter wheel without modification.
that the area of the sample is the same area as the quartz plate, and that the thickness
of the sample is equal to the gap height. We also need to measure the irradiance of
the beam at the cure site which is accomplished with two radiometers.
Radiometers
Certain radiometers may be more or less appropriate for certain sources. For instance, for noncollimated light sources measured irradiance may depend on the angle
of incidence leading to results dependent on the orientation of the probe. Therefore
an integrating sphere style detector is preferred over the flat pan detector style. Since
the technology within both radiometers is proprietary, we focus on contrasting the
specifications that the manufacturers provide and experimental data.
Table 7.1: Comparison of specifications of the Accu-Cal 50 radiometer and the R2000
Radiometer
Power Range Resolution
A range
Radiometer
Accu-Cal 50
320-395 nm
1m2 - 40
1m
Omnicure R2000
250-1000 nm
5mY - 60
5
mW2
Both radiometers have an accuracy of 5%-10%.
The R2000 is a radiometer that is sold in conjunction with the S2000 lamp and
is meant to be used to calibrate the lamp to an absolute intensity. It also serves
to measure the light irradiance emitted from the waveguide. The Accu-Cal 50 is a
radiometer that is sold by Dymax. The advantage of the Accu-Cal is its slim wand
like construction allowing for the evaluation of the irradiation right at the cure site. It
also can be used in a manner similar to the R2000 by screwing the waveguide directly
into the radiometer with the aid of a 5mm waveguide adapter. The two radiometers
have different sensitivities and must be calibrated based on one another (Table 7.1).
Based on the reported wavelength range, the Accu-Cal measures 13.7% of the
spectrum whereas the R2000 measures 96% of the spectrum. We are not told to what
degree the Accu-Cal is sensitive to wavelengths outside of this wavelength range. Not
only does the spectrum to which the R2000 is sensitive match the measured spectrum
25
* uata
-
Fit
E 20 -Linear
215-
:5
10,
LC)
0
0
5
10
15
20
25
Omnicure R2000 Reading (W.cm 2 )
Figure 7-5: The radiometers systematically report different irradiances measured at
the end of the waveguide. The ratio of the two radiometer measurements is constant
over the operating range of the lamp.
of the lamp, the R2000 has been calibrated recently according to NIST standards.
Therefore, we use the R2000 to calibrate the Accu-Cal. To do this we used the 5mm
adapter to the waveguide and measured the irradiance for various settings with both
the Accu-Cal and the R2000. Over this range, the R2000 consistently produced the
lamp setting. The ratio between the two radiometer measurements, see Fig 7-5, is
used to adjust the measurements from the Accu-Cal.
Compact Characterization
We can combine the spectral irradiance of the source, the absorbance profiles of the
materials, and the experimental geometries imposed by the rheometer and sample
volume to calculate t' and i defined in chapter 5 for the two candidate fluids.
Table 7.2: Relevant time constants, t' and t, reported as experimental description
given S2000 polychromatic source and candidate fluids
Nanoparticle Fluid
Micellar Fluid
t'
t
7.2
6.02 x 10 6 texpIr| 2.12 x 10- 6 texpIr
8.08 x 10-5texpIr| 1.47 x 10- 6 texpIr
Rheological Testing
The rheological measurements of the micellar candidate fluid are important for two
reasons. Firstly, rheology is the primary way to evaluate whether a fluid is a good
candidate for a robotic component. Secondly, they provide a means to validate the
proposed model. In this context, the rheological data indicates the change in concentration of the photoresponsive components of the fluid with time. This is not a direct
link between concentration and rheological measurements, because these fluids rely
on a second or third reaction to bring about the rheological change, for instance a
shortening of micelles [30], [18]. While this complexity is a hindrance, we may explore
it in greater detail after the model is validated. For instance, by precisely controlling
the concentration of a relevant species at a particular time, we can study both how
the concentration impacts the rheology and on what time scale that change occurs.
Without our proposed framework, the experimentalist needed to mix up new samples
to study concentration dependence. Now triggering the concentration in the same
way as one triggers a high speed camera may be possible.
7.2.1
Rheometer
The majority of the tests were preformed using an Ares rheometer (TA Instruments),
a strain controlled rheometer, with the parallel plate UV curing accessory described
previously (Diameter D =20 mm, Gap 1= 500pm). A Peltier plate kept the samples
at a consistent temperature of 254C. Dynamic frequency spectra were obtained in
the linear viscoelastic region according to a strain amplitude sweep performed at the
beginning of the test. Most of the experiments involved performing a single shear
flow test or oscillatory test over time while the sample was irradiated. Note that
measuring the rheology of time-evolving materials during curing provides a unique
challenge to rheologists. For instance, as the material changes, the chosen strain
amplitude may no longer guarantee that the fluid is being tested in the linear regime.
Moreover, a particular geometry/material combination that was appropriate at the
beginning of the test may no longer be appropriate at the end of the test when the
fluid has changed significantly. Knowledge of both the initial rheological state and
the final rheological state must be applied whenever possible. Finally, because the
curing process removes the ability to perform the traditional sweeps in frequency or
strain rate, this data must be collected one point at a time and stitched together from
several experiments, to obtain a more complete picture of the fluid.
7.2.2
Small-Amplitude Oscillatory Shear Flow
We briefly describe the collection of rheological data from small-amplitude oscillatory
shear (SAOS). In SAOS, we use the rheometer to impose a small amplitude oscillation
of the form:
2 = o sin(wt),
(7.1)
where 'Yo is the strain amplitude and w is the angular frequency of oscillation. If the
shear strain amplitude, -yo, is sufficiently small, then the shear stress will be linear in
strain and strain rate [4]. We can therefore write
(7.2)
rzY = -A(w)'yosin(wt + 6).
Here A(w) is the amplitude of the stress and 6 is the phase angle between the imposed
strain and the measured stress. We can then separate this oscillating stress into the
component that is in phase with the strain and the component that is in phase with
the strain rate:
r=
-G'(w)-yosin(wt) - G"(w)-yocos(wt).
(7.3)
G" scales the component of the response that is proportional with the strain rate
and is sometimes called the 'loss modulus' for its similarity to a damper. In the
same way, G' scales the component proportional to strain and is sometimes called the
'storage modulus.' We will also chose to relate these components together as a single
component called the complex modulus,
|G*I = v'G 2-+ G"2 = A(w).
(7.4)
This complex modulus relates the stress to the strain. We can also write a complex
viscosity that relates the stress to the strain rate.
The relationship between the
complex modulus and complex viscosity is as follows:
Ir*|
=
1|G*.
(7.5)
For some materials, one may relate the oscillatory data collected to how the fluid
behaves under simple shear flow. To do this one may apply the Cox-Merz rule [4]
which states that the complex viscosity can approximate the shear flow viscosity for
strain rates corresponding to the angular frequency ('(1) =
Inrk =
l'r*|w.
(7.6)
Due to the autocorrelation software employed by the Ares, data was reported every
seven seconds.
7.2.3
Procedure
The material tested in this chapter is the photoresponsive micellar fluid described as
batch D in Table 6.1, composed of 50mM OMCA and 83mM CTAB. Each test began
by checking that the light system was well calibrated with both the R2000 radiometer
and the Accu-Cal 50 radiometer. The light system was then aligned with the installed
UV fixture. The cure site radiometer was used to take a measurement at the position
where the sample would be loaded. The fixture was raised to accommodate the thick
radiometer. Because this meant that the waveguide was no longer aligned squarely
with the fixture window, the waveguide stage was adjusted, and both the first and
maximum reading were recorded. The radiometer was then removed and a micropipette was used to load the ample. By cutting the excess fluid away with a razor
blade, the sample was made to be flush with the upper plate. The waveguide and stage
were then realigned. An experiment was performed usually involving UV irradiation
at a specific irradiation and time. After testing, the sample was removed and the
Peltier plate cleaned.
7.3
Results
In this section we report the results of our experiments. To begin, Fig. 7-6 details the
rheology of the fluid in response to steady shear and oscillatory flows before irradiation
takes place. The fluid is shear thinning, as it has a lower viscosity at higher rates,
and is viscoelastic.
Fig. 7-7 shows the results of steady shear tests at three different strain rates at
101
CD
2- 10
A
T=25*C
10-
0
0
'c
10
.
100
10
1
o
-
G
G'
T=25*C
-
Y.=0. 2
0
...........
. .....
.. I..........
101
100
.. I
102
o (rad/s)
Figure 7-6: a) The steady shear viscosity as a function of shear rate before the sample
(50 mM OMCA and 83mM CTAB) is irradiated, fitted with the Carreau Yasuada
model: rO = 8Pa.s, A = 0.46s, a = 2.79, n = 0.042. b) The dynamic moduli as a
function of angular frequency of the unirradiated sample is fitted with the generalized
Maxwell model: A = 0.41s, gi = 19.2 Pa.
95
constant irradiation. We have demonstrated that we can control the irradiation and
that our results are repeatable. The lower bound of the results are limited by the
torque resolution of the rheometer, Tin = 2pN. Further analysis cannot be completed
using the current experimental setup as a UV compatible geometry such as a quartz
couette cell is not available.
To examine the effects of different irradiances on the evolution of rheology with
time, we expose several samples to increasingly intense beams. Fig. 7-8 details the
storage and loss modulus as a function of time for a fixed frequency of 30 rad/s at
different irradiances.
From this graph, we can see that the rheological properties
are not necessarily linear with concentration as G" rises despite a certain drop in
concentration of the trans-isomer of the photoactive ingredient. The curves from
each irradiance for a given modulus are similar with one another.
We will later
explore whether the model correctly predicts how to scale the time axis to have these
curves collapse together.
7.3.1
Analysis
To compare the theoretical model with the experiments performed, we need to relate
the rheological measurements to the concentration of the photoresponsive species.
We did not perform any concentration studies of the rheology, however. Instead we
will use published data of how the zero shear viscosity changes with concentration of
a similar solution. We reproduce this data as Fig. 7-11 [30].
Possible Application of Constitutive Models
At low shear rates, the material imposes so little stress that the instrument cannot
produce consistent measurements over time while the fluid cures. Therefore we did
not collect how the zero shear viscosity changes as a function of time from our insitu experiments. Instead, we relate oscillation data at moderate frequencies to a
viscosity at corresponding shear rates through the complex viscosity, r*, as detailed
previously.
A range of models can be used to find the zero shear viscosity from
10 1
'
10A
Cd
CL
10~
-
T=25*C
Ir-105mW.cm
120
60
0
300
240
180
Time (s)
-Bt
q=Ae
A(Pa.s
7.56
A
6.56
6.86
A
7.26
A 6.17
A 6.13
A. 1s 7.27
A
Bs
0.030
0.034
0.037
0.043
0.040
0.041
10.051,
10010-
T=25*C
y= 3 s-I
Ir=105mW.cm
0
30
60
90
120
Time (s)
Figure 7-7: a) Time evolution of the steady shear viscosity at different strain rates
for the 50mM OMCA + 83 mM CTAB solution during irradiation. b) Repetition of
the steady shear test on this sample illustrates the reproducibility of data collected
during irradiation. The time constants, have a mean (B) of .0329 s- 1 with a standard
deviation of 6.8x10~3 s-1 and the coefficients have a mean (A) of 6.83 Pa.S with a
standard deviation of 5.63 x10-1 Pa S.
CL
00
10
0
50
100
150
200
250
300
350
Time (s)
118mW.cm2
o 57mW.cm"2
a
142mW.cm
2
311mWcm 2
a 357mW.cm 2
a
T=25 0C
0
0=30 rad.s1
100
-
70=02
0
50
100
150
200
250
300
3!
Time (s)
Figure 7-8: The moduli change over time as a 50 mM OMCA + 83 mM CTAB
sample is irradiated. Here, each experiment corresponds to a different beam irradiance
(measured at the cure site). Lower irradiances lead to longer times required to reach
a desired modulus value, while higher irradiances require less time.
10
A, A
830mM
30m
10~
.I .
102
.
.
a
.e ... a
.
.
1
...21
.
ma
.121
101
100
10-1
..ma
i
1
a ..
.
1
a
a
102
(s -)
Figure 7-9: The shear viscosity as a function of strain rate for different weighted
amounts of OMCA with 60 mM CTAB, re-plotted from Ketner et al [30]. The fit is
to a simplified Carreau Yasuda model with the empirical constants listed in Table 7.3
the complex viscosity, if they are applicable, [4]. For instance, a simplified CarreauYasuada model might be fit to our data as we can assume that the viscosity approaches
zero as we approach infinite shear rates:
-=[1 + (A )"] na.
n7o
(7.7)
This model however involves three fitted parameters: a which describes the breadth
of transition from Newtonian to power-law behavior, n which describes the power law
exponent, and A which determines the shear rate at which the transition occurs from
the zero shear rate plateau to the power law region. The generalized Maxwell model
is also a possible model:
dTk
Tk +
Ak =-
(7.8)
-7k Y
dt
where k = GkAk The small amplitude oscillatory shear material functions satisfying
the generalized Maxwell model are
N
gkAkW
A2 W2 '
G'(w) =
k=1
G"(P)
(7.9)
2
(7.10)
=.Ak
k=1
k
We truncate at k=1 as the first mode is sufficient to capture the low frequency
dynamics. To determine whether either model can be used to predict the zero shear
viscosity, we examine shear flow responses for different concentrations (Fig. 7-9)
and oscillatory responses for tests with increasing exposure (Fig. 7-10). Tables 7.3
and 7.4 show that the fitting parameters for each data set vary with exposure and
equivalently, concentration. Therefore these empirical models are inappropriate to
apply to the data unless each concentration has been fitted separately.
Table 7.3: Fitting parameters for simplified Carreau
Fig. 7-9 of weighted amounts of OMCA and 60 mM
Concentration rjo(Pa s) A (s)
80mM
3.01
0.10
50mM
9.72
0.62
30mM
0.38
0.12
Yasuda model of data shown in
CTAB
a
n
1.27
0
2.02 0.04
1.12 0.35
Table 7.4: Fitting parameters for Maxwell model for data shown in Fig. 7-10 and
the resulting zero shear viscosity. The sample is initially 50 mM OMCA + 60 mM
CTAB and then undergoes irradiation for the time specified.
Exposure gi (Pa) A, (s) qo = giA, (Pa s)
0 min
16.47
0.41
6.75
5 min
10.66
0.32
3.41
15 min
6.91
0.25
1.72
100
.
I
Increasing Expure
xposure
.
0--- 0
101
IE
PIu ~
Cu
0-
100
o
o
o
G'
0
0
=
G"
Y0= 0.5
T = 25*C
101
.
.
.
.
.
.
.
101
100
.S
.a
a.
I
102
co (rad/s)
Figure 7-10: Exposure of 50 mM OMCA + 60 mM CTAB sample by an uncharacterized UV lamp for set periods of time. A Maxwell model is fit to each curve with
parameters listed in Table 7.4.
101
Approximation of Viscosity as Zero Shear Viscosity
In order to use the concentration analysis completed by [30], we must find another way
to determine the zero shear rate viscosity besides the application of the above models.
In the future, we plan to measure the complex viscosity at the given frequency for
varying concentrations therefore mapping what concentration is implied at a given
material property. In the absence of this, we make the crude approximation of the
viscosity at a corresponding strain rate to 30 rad/s is approximately equal to the zero
shear viscosity. Our irradiation experiments, first introduced in Fig. 7-8 were carried
out at this angular frequency and motivate this choice.
This is a coarse approximation as the fluid has already been identified as a shear
thinning fluid. Using the empirical fit between zero shear viscosity and concentration
in Fig.7-11, we estimate the final concentration of trans-OMCA of our samples during
irradiation. We use this as a lower bound of our data. As an upper bound, we note
that this method underpredicts the initial concentration given the measured complex
viscosity. We take the difference between this predicted initial concentration and the
known initial concentration and use this as a correction to achieve the upper bound.
The error bars described are illustrated in Fig 7-12 for the final points of the SAOS
experiments in Fig. 7-8. We take the average of the bounds in concentration to
choose the scale with which to compare our concentration and our complex viscosity
measurements in Fig 7-13. This scaling implies that q* = (.0 0 5 )1 0 44.29[OMCAtrans] and
is used again in Fig. 7-17.
We note that the shear flow experiments taken at a strain rate of 3 s 1 in Fig. 7-7,
provide a better estimate of the evolution of the zero shear rate viscosity, although
we do not have the experiments at various irradiance for this experimental condition.
Again using the empirical relation derived from [30], we similarly relate viscosity to
concentration in Fig. 7-15 by the relationship 1 = (1.23 x
102
10
-3)1 0 76.27[OMCAtrans].
M
102
101
100
1.1.1.1.
"
7 o =Ae&B[S]
"
U
0
U.
A=2x1O- Pa.s
B = 0.4 M~
R2=.98
*1
C')
a- 10-1
0.
10-2
10-
0
I
I
-
I
I
-
I
I
i
-
I
S
-
I
i
-
I
i
-
I
i
-
I
I
10 20 30 40 50 60 70 80 90
[S] (OMCA mM)
Figure 7-11: Data describing the relationship between weighted amounts of transOMCA + 60 mM CTAB concentration and zero shear viscosity reported in Ketner
et al [30]. Using an exponential fit, we approximate a relationship between the concentration of the OMCA and the viscosity to be used in our comparisons between
experiment and theory.
103
I
I
I
I
I
I
-
I
T'
I
0.05
T
0.04
C
0.03
E
Experimental:
o Data
0
Theoretical:
0.02
297-357 mW cm 2
245-311 mW cm-2
0.01
0.00
I
0
50
100
150
.
200
I
250
109-142 mW cm-2
27-57 mW cm-2
-I
- 5-26 mW cm-2
300
350
400
Time (s)
Figure 7-12: Estimation of final concentration of OMCA from the rheological data
taken and relationship derived from Fig. 7-11. This is then compared to our model's
prediction of the concentration given the experimental conditions.
104
0.05
0.04
0.03 -
0.1
Experimental:
o Data
Theoretical:
0.02 -:297-357
a
mW cm-2
245-311 mW cm-2
a109-142 mW cm-2
0.01
27-57 mW cm-2
*5-26 mW cm
0.00.
0
50
100
150
200
250
300
350
-20.01
400
Time (s)
Figure 7-13: Comparison of complex viscosity, r;*, experimental data with theoretical
prediction. The concentration and complex viscosity axis have been scaled to reflect
the empirical relationship between concentration and r*.
105
Comparison between prediction and experiment
The colored swaths in Fig. 7-12 and Fig. 7-13 were generated using a standard
numerical solver applied to the nonlinear differential equation, Eq. (5.4). We used
the first and the maximum irradiance measurements recorded by the radiometer as
bounds for the irradiance for each trial, with the exception of the lowest irradiance
test where the error tolerances of the radiometer and the maximum measurement were
used. These swaths are in reasonable agreement with the experimentally measured
complex viscosities. After noting that the experimental data fall in the linear portion
of the evolution of the concentration, we choose to scale the moduli in Fig 7-8 linearly
by t' as in Fig. 7-14. The regions where the experimental curves do not overlap may be
because the data acquisition software captures a measurement only every 7 seconds.
This would affect the higher irradiance trials predominately which is reflected in Fig.
7-14. The agreement between curves indicate the suitability of the t' scaling as well
as the repeatability of the experiment. These figures in addition to Fig. 7-13 are
taken as validation of the polychromatic form of our model.
7.4
Limitations and Extensions
In this section we provide a brief set of examples of the rich exploration that can be
done with in-situ photorheological testing in conjunction with the concentration data
predicted by our model. Specifically we present 'dose' experiments and a comparative
study of irradiation with a temperature ramp as a means of studying micelle dynamics.
7.4.1
Dose Experiments
Beyond validation, the in situ tests can provide a window into the chemical and microstructural dynamics of a fluid. In addition to the time evolution experiments, we
also irradiated the sample for specific lengths of time and recorded the material response after the light source was turned off. By conducting these 'dose' experiments,
we investigate the validity of assuming that the chemical dynamics of the photore106
I
I
118mW.c-2
57mW.cni 2
* 142mW.cm-2
a 311mW.cm 2
m 357mW.cm-2
£
0. 10
T=25"C
w=30 rad.s~
7.=0.2
100 L
0.0
0
0.05
0.10
0.15
0.20
0.25
0.30
0.20
0.25
0.30
t'
i'
100
0.00
0.05
0.10
0.15
Figure 7-14: The evolution of moduli during irradiation with time axis scaled to t'.
In contrast to Fig. 7-8, the data has collapsed onto characteristic curves.
107
sponsive species are either the only or the limiting dynamics with respect to material
response. In Fig. 7-15, Fig 7-16, and Fig 7-17, we see a significant recovery upon
the interruption of irradiation. This may be due to the concentration of the transOMCA increasing, or the re-assembly of worm like micelles. The cause of the recovery
remains an open question for future research. These experimental results limit the
application of our model by showing that the sample has dynamics that our model
cannot predict: although we note the ability of the model to describe the material
response before the source is turned off. On the other hand, these results uncover
an opportunity to study chemical and microstructural dynamics. Assuming that the
model presented here is correct, the rheologist can study the dynamics of the wormlike micelle lengthening and shortening upon the introduction of a concentration of
cis-OMCA.
7.4.2
Temperature Sweep versus Irradiation
Comparing the evolution of dynamic moduli over time during irradiation (for a total
duration of 100 s) and that of a temperature sweep, as in Fig. 7-18, we suggest that
the process the micelles go through during irradiation could be similar to the process
they go through when heated, i.e. the micelles shortening. The graphs are so similar in
fact, we initially worried that our experiments might be examining how UV irradiation
heats the sample rather studying a photochemical reaction. We used three procedures
to ensure that that was not the case. First we used an IR thermometer to verify the
Peltier plate and the quartz plate were at 25 0 C. A thermal camera was then used
to image the sample and the rheometer. We found that over a 10 minute time span
the region of interest did not change more than half a degree. Finally, we performed
similar tests on an 83 mM CTAB +50mM of NaSal (Sodium Salicylate) sample which
forms a similar fluid to the CTAB+OMCA solution, though it is not photoresponsive.
We performed irradiation and a temperature ramp during shear flow experiments. If
the UV light was causing the fluid to heat up, we would have seen this fluid behave
as if it were responsive to light. This was not the case as the rheological properties
of the sample remained constant throughout the test. Therefore, the temperature
108
0.05
0.04
100
Experimental
T=25"C
-1- -
y= 3 s
lr=10O5mW.cm -2
0
A
30 s0
A&
60 s
A
A
90 S
120 s
heoretical
2
-
0.03
-105-107 mW cm21
100 200 300 400 500 600
700 800
Time (s)
Figure 7-15: After doses of irradiation, the sample recovers. Open triangles indicate
that the measurements were taken despite being below the stated torque resolution
of the ARES rheometer. The initial evolution of the viscosity is compared with the
theoretical prediction of the concentration.
109
*
*
*
*
30s
60s
90s
120s
104
a
m.F
m=30 rad.s"
yO=0.2
-
lr=88mW.cmI
0
.
I
I
*
I
I
.
I
1
I
60 120 180 240 300 360 420 480 540 600
Time (s)
101
0
60 120 180 240 300 360 420 480 540 600
Time (s)
Figure 7-16: The moduli are examined after doses of irradiation are delivered. After
the irradiation is stopped, the sample partially recovers.
110
0.05
*
**
***
*****
-**
**
* ***
**
*
0.04
0.03
10~
Expermental:
*
*
*
*
10-2
0.02
30s
60 s
90s
120 s
0
T=25 0C
ca=30 rad.s'
y8=0.2
Theoretical
51-88 mW cm-2
0.01
Ir=-88mW.cm-2
0.00
120
60
180
Time (s)
Figure 7-17: The measurement of complex viscosity from the dose experiments is
compared to the theoretical prediction of concentration through the process described
in section 7.3.1.
111
response and the exposure response did not superimpose, and we see this to be a
feature of the photoresponsive micellar system only. This may also provide evidence
that the dynamics seen in the UV dose experiments are related to the lengthening
and shortening of the micelles on an experimentally relevant timescale.
7.5
Summary
We have validated our model with experimental results using a polychromatic light
source. We have demonstrated how we can compactly and comprehensively describe
our setup in a way that other groups can replicate our results even if they do not have
the same light source. Now that we have an ability to predict the concentration of
the photoactive component during a rheology experiment, we have explored possible
avenues of research into microstructural dynamics of a sample given the knowledge
of how the concentration of an internal species changes.
112
[OMCAt a] (mM)
35
40
45
50
Ir=57 mW.cm-2
T=25*C
10
0~0
e=G"
o=30 rad/s
yO=0.2
10
0 1
1
26
1
28
I
30
I
I
32
.-
I
34
1
36
38
T (CC)
Figure 7-18: Comparison of dynamic moduli of a 50 OMCA + 83 CTAB sample undergoing a temperature ramp without irradiation (bottom axis) and under irradiation
causing the concentration at constant temperature of trans-OMCA to decrease (top
axis). The scaling of the two axis is 1.23 mM per 'C. During the 100 second interval
of irradiation the absorbed energy was calculated to be approximately 1 J.
113
114
Chapter 8
Robot Application
In this final chapter we discuss how these findings impact potential robotic applications. We also suggest desirable features of a photoresponsive fluid for material
scientists and chemists who wish to develop fluids more appropriate for our application.
8.1
Feasibility of Current Photoresponsive Fluids
for Autonomous Robots
While in previous chapters we focused on a lab scale UV lamp, we now evaluate light
sources appropriate for robotics. Fig 8-1 shows the spectral power for a FOX UV
LED. This UV LED has a total intensity of 50pW and a corresponding irradiance of
approximately 29w.
Table 8.1: Relevant time constants, t' and i, of 8pL of micellar fluid irradiated with
LED compared to 160 pL of nanoparticle fluid irradiated with S2000.
Micellar Fluid
Micellar Fluid Nanoparticle Fluid Nanoparticle Fluid
LED
S2000
LED
S2000
t'
i
1.34 x 10-4texp
5.6
x
10-4texp
9.49
1.27
x
x
10- 3texp
10
-
texp
1.45 x 10 4 texp
1.07
x
10
5
tep
3.34 x 10- 3texp
2.32 x 10- 3 texp
Using our compact notation we can adequately describe the conditions of our
115
1.8
1.6 -
E 1.4C
1.2-
1.0 M
0.68
50 pW UV-LED
0.
I.. 0.6-0.4M 0.0
Co
200
250
300 350 400
450
500 550
600
X(nm)
Figure 8-1: Spectral power of a UV-LED (FOX) measured by the Ocean Optics
USB2000 Fiber Optic Spectrometer.
experiment in Table 8.1. We have duplicated Table 7.2 within this table with the
average lamp irradiance 1.6W used in the irradiation studies presented in chapter
7 to aid comparison.
Note that we are comparing, different volumes of different
concentrations of materials with different absorption spectra irradiated with different
light sources with different relative spectral intensities and overall irradiances. Prior
to this work, the author does not know of a similar technique to compare vastly
different photoactive materials irradiated with a broad spectrum of light sources.
We present the calculated switching times of two of our candidate fluids achieved
with the characterized UV LED in 8-2. The long switching times (hours) suggested
by Fig 8-2, lead us to conclude that even with small volumes of fluid with an ideal
<} = 1, photoreological fluids are not feasible with an autonomous robot equipped
with LEDs.
116
M
8pL of:
0.-0.8
50mM OMCA
13mM PAG
--
.0
0.4
02A4 mm'
:46m
- 0.2.0.4
0
-
1
2
3
50pW LED
- -
-
-
-
5
4
6
7
8
-
9 10 -11 12
Time (hours)
Figure 8-2: The evolution of the material composition during irradiation from an LED
for two candidate fluids with a photoactive species concentration of 50 mM OMCA
and 13 mM PAG respectively. Note that both fluids require hours of irradiation to
convert half of the photoactive species.
117
8.2
Designing Future Photoresponsive Fluids for
Fast Switching Times
While the photoresponsive fluids examined here are inappropriate for autonomous
applications that require swift transitions between states, we explore in this section
the attributes that would be desirable if we had the ability to design a photoresponsive
fluid. We also present when and how tuning the experimental conditions will impact
the speed of reaction for a given fluid.
There exist a large number of mechanisms that lead to the rheology and the change
in rheology of a material, and an even larger number of mechanisms involved in any
observable change such as physical, mechanical, optical changes. It is impossible to
describe how best to tune the fluid for speed without knowing how the addition or
reduction of a particular component interacts with the rest of the fluid. In particular,
for the model introduced, there is a large difference if the property of interest is
dependent on the absolute molar concentration of the photoactive species that are
in a particular form (for instance the molar concentration of cis-isomer) or if it is
dependent on the percentage of the photoactive species that are in a particular form
(for instance the ratio of cis-isomer to trans-isomer). Which quantity is more relevant
will depend on the nature of the dynamic balance between the photoactive species
and other chemically significant components in the material.
Firstly, the ideal photorheological fluid would have a large physical change with
the introduction of either a small amount (moles or molar) of the activated species or
a small percent change in concentration of the activated photoresponsive species. For
example the transition would be complete when 1% of the trans-isomer transitions
to its cis-isomer form. Another example would be that the transition is complete
when 1 mM of the cis-isomer is present. The application of this fluid would center
around this transition by considering this concentration or percent concentration as
an operating point.
How fast this transition occurs depends on the magnitude of the absorbance of
the fluid. To begin, we assume that the transition depends on the absolute number of
118
moles or concentration of the photoactive fluid. There are two regimes of response of
any photoresponsive fluid, a regime where the concentration decreases linearly and a
regime where the concentration decreases exponentially (as originally noted in Table
7.1).
Because the time constant of the exponential decay is very small, the same
absolute increase in concentration will take longer in the exponential regime than in
the linear regime. Ideally both the initial and final states of the fluid would place
the operation of the fluid in the linear regime. To do this both states must have
an average absorbance, i.e. product of the concentration, molar absorptivity, and
thickness of the sample, above 5, as discussed in Section 5.2. Given a typical molar
absorptivity of 640 McL
at 365 nm for trans-azobenzene and a sample thickness of
1 mm, both states should have a concentration of photoactive species greater than
80mM. The time constant within this linear regime, t', then is adversely affected by
large volumes and positively affected by large surface areas. Keeping in mind the
requirement of a large absorbance for this regime, increasing the ratio of the area to
the volume, e.g. making the fluid film thinner, will speed the reaction.
Alternatively we could assume that the transition depends on the percent increase
of the activated species. If the initial concentration in the fluid is small, a demanded
increase in the percent concentration of the activated species translates to a very
small absolute change in concentration. Therefore, even though the time constant
of exponential decay is very small, the same percent increase in concentration will
take a shorter amount of time in the exponential regime than in the linear regime as
the absolute change in concentration is small enough to offset the slower response.
Whether desired or mandated by a low molar absorptivity or low photoactive species
concentration, the fluid may evolve in the slower exponential regime. The response of
the fluid can be quickened predominantly by increasing t within this regime. Seeking
a large molar absorptivity is the only factor besides a well matched source with a
large irradiance that is controllable that will speed the reaction. In this regime, the
smaller the initial absorbance the less the thickness of the film impacts the speed of
the reaction.
For the special case of a monochromatic light source and an interest in 95% conver119
sion of the photoactive species, we may use the monochromatic curve, Eq. (5.15), to
derive two helpful representative decay times. For solutions with initial absorbances
above 1.05, 95% of the photoactive solution is converted at
'5
tl
0.05
=
SolNA hc
.olA
Ir
A~
(8.1)
For solutions with initial absorbances below unity, 95% of the photoactive solution
(with an error of at most 3% at absorbances close to unity) is converted at
0.0223
4=
(8.2)
-.
IrEA
A
We can therefore summarize the discussion with Table 8.2 describing what parameters
affect the speed of reaction for a fluid given the initial absorbance of the fluid.
Table 8.2: Parameters which tune how quickly the sample reaches 95% conversion
for: SoeAl < 1
45 =
0.0223-IrEA
NA
for: SoEAl > 1.0256
t'e
95r =
A
" doubling Ir halves 495
" doubling eA halves t45
0 . 0 5 SO'
hc
A
o doubling Ir halves t'5
e halving So halves t'5
o halving 1 halves t'5
The above description is most intuitive for the monochromatic light source, but
should also provide guidance for a polychromatic source as well. Of course in either
case we have assumed that the light source is well matched to the absorbance spectrum
of the fluid. Ideally the emission spectrum of the lamp would overlap entirely with
the absorbance spectrum of the fluid, including having its peak at a wavelength that
is also a strongly absorbed wavelength. Given that most commercially available LEDs
have wavelengths greater than 350 nm, the fluid should also be strongly absorbing
above 350 nm. We have also assumed throughout that the area of the sample and
that of the incident beam is the same, that thickness and opacity of the solution is
such that the irradiance at the middle of the sample is the same as at the top of the
120
sample, as well as that the quantum efficiency of the fluid is maximized.
We have already discussed some of the criteria concerning the more complicated
reversible photorheological fluids. The criteria on the molar absorptivity of the two
species and the spectral irradiance of the source in order for the fluid to have a reversible transition between states is of first importance, followed by the ratio in Eq.
(5.46) describing the photostationary concentration. The dynamics are complicated
enough that a recommendation for tuning the dimensionless time related to a reversible fluid and a polychromatic source,t, is not made beyond stating its definition.
8.3
Summary of Governing Equations and Other
Relevant Quantities
We recommend reporting the spectral irradiance of the light source and molar absorptivity, volume, area of the sample exposed to the beam, and concentration of the
photoactive species as a standard minimum set of variables. With these quantities a
broad range of relevant quantities can be calculated such as the energy the sample has
absorbed and the number of molecules that transition as a result of this process (Table 8.3). We have put forward a model, presented in Chapters 2 through 5, that can
be used to predict how a photoactive species evolves under the irradiation of a variety
of sources with time. This is summarized in Table 8.4 for fluids where each molecule
transitions after absorbing a photon. We then developed an exact solution for the
concentration as a function of time for the monochromatic source and irreversible
fluid case and approximations for this in regimes defined by the absorbance of the
fluid , summarized in Table 8.5 for the fluids with only one photoactive component
and in Table 8.3 for fluids with two absorbing species. These results are intended
to aid in comparison of the responses of photoresponsive fluid and guide application
specific design decisions.
121
Table 8.3: The energy absorbed and the number of molecules converted during an
exposure period
EA
fT
Iri(A, t)(1 - 1O-E(A,t)[S](tl)dt dA
r:
Areaj
Ii(
t)
Nm =jAmax j Ir(,t(Areai
.>
O(At[]t(A
~-td
td
0o
Table 8.4: Summary of governing equations for irreversible and reversible fluids for
monochromatic and polychromatic sources (4=1)
Species
[S]
Light Source
Differential Equation
d[S]
=
dt
d[S]
[S] olyhroaN
[5
Plyhrmaic
dt
Monochromatic
_
[A], [B]
Monochromatic
[Al, [B]
Polychromatic
d
di
dt
=t
A
Area
N
IriA(1 - 10~e\l[s]) dA
NAV
hc
Area2 Amax
1r2 (A)(1 - lO-E(-')1SI()k-dA
NAV lmjn
hc
I
Area IrAA(lO-1[^1 + 1OEAI[B])
NAVhc
]
- Area
N Vhc A,,n
122
IrA A(-1O-EA(A)1[A]
+ 10-B(A)l[B)dA
Table 8.5: Summary of solutions and dimensionless numbers for illumination of irreversible fluids (<D=1)
[5 =logio
Monochromatic
((10SIo
- 1)10- + 1)
=
C[S]
l
= texp
eri,\c\
A
NA hc
Polychromatic:
eC[S]l >
'eA[S]l <
-t' + 1
S
1
10-1
S
(1
te
t'
30-
= tex
=L
_
s
- 109
VS 0
1
NA
Anx
fAmin
jmS
ax
Amin
A) dA
IrA cyd
Ir(A) e(A)A dA
hc
NA
Ir(A)Ae(A) 2 dA
Sof
021Saxi(10)l
2
f"ma Ir(A)AE(A)dA
_
01
Table 8.6: Summary of approximate solutions and dimensionless numbers in the limit of small absorbances for illumination of
reversible fluids (4=1)
Monochromatic:
[A]
A = CAA
Polychromatic:
[A]
=
+ EBA
=
(1 - #5 ) 10- + OA
-
[Al = [Ao]
[t
= texp
#-
N IA
=A
(eBA) 2ln(10)Aol
(1 - #(A))10- + #(A)
((A) = CA (A) + EB (A) - (EB (A)2 ln(10)Aol
[A]
=
f
= te
B
Am"x
Ir(A)((A) A
-dA
ma
pAmi
NA
hc
#(A)
J'"
=mi
fa
"
f'i
Ir(A)EB(A)AdA
Ir(A)((A)AdA
8.4
Conclusion
The goal of this thesis was to determine if photorheological fluids are appropriate for
our robotic application. Since the engineering tools necessary to answer this question were not apparent, we developed models and metrics to describe the chemical
dynamics and quantify relevant parameters effecting the speed of the rheological transition. Our metric is applicable to lamp characterization, predicting rate equations,
and comparing between very different photorheological fluids. We have shown that
our metric describes published data for monochromatic sources, and experimental
data obtained from polychromatic sources. We recommend that the metric is further
examined for the broad cases of reversible fluids and fluids where two species have
comparable molar absorptivities.
On the robotics side, we determined that, given
current technology and materials, photorheological fluids are not feasible for small
scale autonomous robots where the stimulus input is based on a typical UV LED.
In the meantime, we recommend the continued use of energy metrics such as the
expression in Table 8.3 to find and optimize other active fluids. We note that given
the increased interest in photorheological fluids for a variety of applications and the
manufacturing trend towards increased intensity of LEDs and lower wavelength, new
materials may become available making it necessary to revisit this design decision.
We have also provided a description of what attributes a new fluid would need to be
desirable for this application. To aid swift adoption of new materials and technology,
we encourage researchers to report the spectral characterization of their source and
responses using the methods put forward in this thesis. Finally, we recommend the
continued support of innovative robotics programs that push scientists to look at their
problems in new ways.
124
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October,
LC-1222,
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3M
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